Methods for volumetrically controlling a mixing apparatus

ABSTRACT

Methods of controlling a volumetric ratio of a material to total materials in a mixing vessel are provided. In various embodiments, the methods may comprise: estimating the volumetric ratio of the material to the total materials in the mixing vessel and an output flowrate of the material from the mixing vessel using a volumetric ratio observer; dynamically recomputing the commanded input flowrate of the material based on outputs of the volumetric ratio observer using a flow regulator; and adjusting an input valve of the material based on the commanded input flowrate of the material using a flow modulator. The mixing vessel may include a first mixing vessel partially separated from a second mixing vessel. In this case, a height of the total materials in the second mixing vessel may be estimated using a height observer.

BACKGROUND AND SUMMARY OF THE INVENTIONS

The present invention generally relates to process control, and moreparticularly to methods of volumetrically controlling a mixingapparatus.

The following paragraphs contain some discussion which is illuminated bythe innovations disclosed in this application, and any discussion ofactual or proposed or possible approaches in this section does not implythat those approaches are prior art.

The following applications filed concurrently herewith are notnecessarily related to the present application, but are incorporated byreference herein in their entirety:

“Methods of Determining a Volumetric Ratio of a Material to the TotalMaterials in a Mixing Vessel” (U.S. application Ser. No. 11/323,831,filed simultaneously with the effective filing date of the presentapplication)

“Systems for Determining a Volumetric Ratio of a Material to the TotalMaterials in a Mixing Vessel” (U.S. application Ser. No. 11/323,323,filed simultaneously with the effective filing date of the presentapplication), and

“Methods of Volumetrically Controlling a Mixing Apparatus,” (U.S.application Ser. No. 11/323,324, filed simultaneously with the effectivefiling date of the present application).

Control systems are currently being employed to control processes formixing together multiple components in a mixing vessel. An example ofsuch a process is mixing together dry cement and water to form a cementslurry for use in well cementing. Well cementing is a process in whichwells that penetrate subterranean formations are formed in the earth,allowing natural resources such as oil or gas to be recovered from thoseformations. In well cementing, a wellbore is drilled while a drillingfluid is circulated through the wellbore. The circulation of thedrilling fluid is then terminated, and a string of pipe, e.g., casing,is run in the wellbore. Next, primary cementing is typically performedwhereby a slurry of cement in water is placed in the annulus, which islocated between the exterior of the pipe and the walls of the wellbore.Within the annulus, the cement slurry is allowed to set, i.e., hardeninto a solid mass, to thereby attach the string of pipe to the walls ofthe wellbore and seal the annulus. Subsequent secondary cementingoperations, i.e., any cementing operation after the primary cementingoperation, may also be performed. One example of a secondary cementingoperation is squeeze cementing whereby a cement slurry is forced underpressure to areas of lost integrity in the annulus to seal off thoseareas.

Conventional control systems for such a cement mixing process oftenattempt to control the output flowrate and output density of the mixtureexiting the mixing process by controlling the positions of input valvesinto the system. In the example in which the input valves are an inputwater valve and an input cement valve, an output slurry densitymeasurement and a total output flowrate measurement are commonly used tocontrol the process. A Proportional-Integral-Derivative (PID) controllermay be used to calculate the commanded input water flowrate based on thetotal commanded input flowrate and the commanded slurry density. It mayalso be used to calculate the output water flowrate based on the totalmeasured output flowrate and the measured slurry density. Further, a PIDcontroller may be used to calculate the commanded input cement flowratebased on the commanded total input flowrate and the commanded slurrydensity. Moreover, it may be used to calculate the output cementflowrate based on the total measured output flowrate and the measuredslurry density. However, this type of control system has a majordrawback in that the response of the water and cement control loops aretime lagged. Thus, a change in the water flowrate usually is notobserved and corrected for by the cement control loop for some time andvice versa. As a result, oscillations in the density and flowrate may beexperienced, especially during transitional phases such as an inputdisturbance or a commanded change. Another drawback of this controlsystem is that often no densitometer is available to measure the outputslurry density, or the output slurry density is ill-conditioned to beused as a control variable (i.e., the value of the density of onecomponent being mixed is very close to the value of the density of theother component being mixed in a two-component system).

The physical system being controlled (e.g. the mixing process) typicallyexhibits some nonlinear behavior. Using a PI or a PID control system toovercome the physical system nonlinearity results in eigenvaluemigration. That is, the eigenvalues, i.e. the parameters that define thecontrol system, are dependent on the operating conditions such as theflowrate and thus experience relatively large shifts in value as theoperating conditions change. Unfortunately, the system is a coupledsystem in that different portions of the system depend upon each other.Thus, fine tuning the control system is typically impossible toaccomplish due to the differing time- or frequency-domain responses ofthe different portions of the system.

In addition to these limitations, the mixing process often experiencesdisturbances that can lead to inaccuracies in the measurements of theprocess. Such disturbances include oscillations in the height of thefluid in the mixing vessel, particularly when the mixing vessel is inmotion such as in a ship-based mixing process. Another disturbancecommonly encountered is that one material, e.g., the dry cement, maybecome plugged in the pipe being fed to the mixing vessel such that asignificant amount of air is required to force the material into themixing vessel. As such, the fluid in the mixing vessel may containunaccounted for air.

A need therefore exists for a control system capable of controlling theoutput flowrate and composition of a mixing process without needing tocontrol or measure the output density of the process. Further, it isdesirable to reduce the lag-time of the control system, allowing theprocess to be monitored and controlled in real time with more accuracyand precision. It is also desirable that the control system be capableof more robustly accounting for disturbances, nonlinearities, and noisethat may occur in the mixing process.

Methods of Volumetrically Controlling a Mixing Apparatus

Some teachings and advantages found in the present application aresummarized briefly below. However, note that the present application maydisclose multiple embodiments, and not all of the statements in thissection necessarily relate to all of those embodiments. Moreover, noneof these statements limit the claims in any way.

The estimated volume of a material to total materials in a mixing vesselmay be determined using a volumetric ratio observer comprising afeedback loop. The volumetric ratio observer advantageously provides forfiltered, zero-lag estimations of the actual volumetric ratios withinthe mixing vessel in a manner that accounts for unwanted disturbances inthe system. By way of example, the materials being combined in themixing vessel may be dry cement and water, and the slurry formed thereinmay be pumped down a wellbore during a well cementing process. Knowingthe relative volumes inside the mixing vessel at any time and thus therelative volumes of the cement and water being pumped downhole may bevery useful.

The volumetric ratio observer may also be employed to estimate thevolumetric ratios of the components in two or more mixing vessels inseries that are separated by weirs or any other channeling devices thatallow fluid to pass from one vessel to the next. The volumetric ratioobserver desirably may be used in a control system of such a mixingprocess where the density of the slurry mixture is unavailable. It mayalso be employed to control the mixing process even if the densities ofthe materials being mixed are near the same value such that adensitometer cannot clearly differentiate between them. The volumetricratio observer allows the mixing process to be controlledvolumetrically, providing for tighter control over the relative volumesof the materials in the mixing vessels. As a result, the process may beoptimized such that the overall cost of the process is minimized.

Systems for controlling such a mixing process may include multiplevolumetric ratio observers (also referred to as volumetric estimators)for estimating the volumes of the respective components in the mixedproduct and a feedback block for combining at least one physicalmeasurement of the mixed product with the estimators to provide a closedloop system. That is, the respective estimated volumes may be improvedby feeding a correction based on one or more physical measurements ofthe system to the volumetric ratio observers. Examples of physicalmeasurements include measurements of the height, density, total weight,and viscosity of the mixed product.

As described previously, the physical system, i.e., the mixing process,may be affected by nonlinearities. In particular, the feedback of thephysical system may be nonlinear, making it difficult to control. Toovercome this problem, a virtual system may be simulated in real-time,wherein the virtual system i.e., the system “seen” by the controlsystem, represents the physical dynamics without the nonlinear physicalsystem feedback. The physical system may be controlled with reference tothis virtual system by simply using a proportional controller, resultingin more stable eigenvalue behavior than if the physical system werecontrolled by a PI or PID controller.

The outputs from the control loop employed to control the virtual systemmay be used to control at least one low-level control loop that controlslow-level inputs to the physical system. The low-level inputs may be,for example, the positions of valves through which the respectivecomponents flow into the mixing process. In a first process, high-levelcommanded inputs (e.g., the height of the fluid or the volumetric ratioof one component to total components) may be converted into intermediatecommanded targets (e.g., the total input flowrate and the input flowrateof one component). In at least one additional process, thoseintermediate commanded targets may be converted into the low-levelcontrol inputs or settings described above. In various embodiments, adisturbance value is fed back into the first process to decouplenonlinearities. In more embodiments, the desired or measured value ofthe total flowrate of the mixed product may be fed forward to decouplethe effects of the output flow.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 depicts a mixing apparatus comprising two mixing vesselsseparated by a weir.

FIG. 2 is a state block diagram of an embodiment of a physical systemand a flow modulator being used to volumetrically mix components in themixing vessels shown in FIG. 1.

FIG. 3A is a state block diagram of an embodiment of a portion of avolumetric ratio observer for use with a single mixing vessel.

FIG. 3B is a state block diagram of another embodiment of a portion of avolumetric ratio observer for use with two mixing vessels.

FIG. 4 is a state block diagram of an embodiment of a control system forcontrolling the mixing apparatus depicted in FIG. 1.

FIG. 5 is a state block diagram of another embodiment of a controlsystem for controlling the mixing apparatus depicted in FIG. 1.

FIG. 6 is a state block diagram of yet another embodiment of a controlsystem for controlling the mixing apparatus depicted in FIG. 1.

FIG. 7 is a state block diagram of yet another embodiment of a portionof a volumetric ratio observer for use with mixing three componentsutilizing a two-vessel mixing apparatus.

FIG. 8 is a state block diagram of still another embodiment of avolumetric ratio observer for use with mixing three components utilizinga two-vessel mixing apparatus.

FIG. 9 shows how a process for mixing multiple components in a mixingapparatus comprising a single vessel or tank can be controlled using avolumetric ratio mixing control scheme.

FIG. 10 shows results obtained from systems according to FIGS. 2-9.

FIG. 11 shows yet another embodiment, with a different implementation ofthe disclosed volumetric control ideas.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Physical System Model

The physical system considered here is a mixing apparatus comprising twomixing vessels 10 and 12, e.g., tanks, separated by a weir 14 as shownin FIG. 1. It is understood that weir 14 may be replaced by other formsof channeling fluid from mixing vessel 10 to mixing vessel 12. As usedherein, a “mixing vessel” is defined as a structure that can holdmaterials as they are being mixed together. Further, a “weir” is definedas a structure that at least partially separates two mixing vessels suchthat it allows fluid to flow between the two vessels. The mixing processmay be carried out through the action of rotating paddles 16 and 18 inrespective mixing vessels 10 and 12. Two different materials may beseparately added to mixing vessel 10 through pipes 20 and 24. Valves 22and 26 may be disposed in respective pipes 20 and 24 for controlling theflow of the materials into mixing vessel 10. Within mixing vessel 10,the two materials are mixed together using rotating paddle 16. Themixture formed in mixing vessel 10 may then flow over weir 14 intomixing vessel 12 where the mixing process continues with second rotatingpaddle 18. The mixture in mixing vessel 12 is finally pumped out of themixing apparatus through an output pipe 28 in which a pump 30 isdisposed. The mixing system depicted in FIG. 1 may reside on the ground,on an oil platform, or on a ship.

In the embodiment depicted in FIG. 1, water and dry cement are thematerials being subjected to the mixing process. It is understood thatin other embodiments, liquids other than water and dry additives otherthan cement could be subjected to the mixing process. The volumetricflowrates of the water and the dry cement supplied to mixing vessel 10are represented in FIG. 1 as {dot over (V)}_(w) and {dot over (V)}_(c),respectively. The mixing apparatus may be capable of mixing the drycement and the water to a desired density at a desired volumetricflowrate as required for use in oil well cementing applications.Additional parameters shown in FIG. 1 include the volumetric slurryflowrate {dot over (V)}₁₂ over the weir from mixing vessel 10 to mixingvessel 12, the slurry height h₁ in mixing vessel 10, the output slurryrate {dot over (V)}_(s) from mixing vessel 12, and the slurry height h₂in mixing vessel 12. In various embodiments of the mixing apparatus, theapproximate values for these parameters of the actual physical systemare as follows:

-   -   {dot over (V)}_(s) ranges from about 1 bbl/min (barrels per        minute) to about 15 bbl/min;    -   ({dot over (V)}_(w)/{dot over (V)}_(s)) ranges from about 0.3 to        about 0.90;    -   h₁ is approximately 4 ft. as defined by the weir height;    -   h₂ is approximately controlled to 3.5 ft.;    -   h₁A₁ is approximately 220 gallons; and    -   h₂A₂ is approximately controlled to 175 gallons.        In alternative embodiments, the mixing apparatus may be designed        to run at a {dot over (V)}_(s) of up to 100 bbl/min.

The physical system can be modeled mathematically using the law of massconservation in a control volume, which is represented for mixing vessel10 by the following equation:ρ_(w) {dot over (V)} _(w)+ρ_(c) {dot over (V)} _(c)−ρ₁₂ {dot over (V)}₁₂ +{dot over (m)} _(D)={dot over (ρ)}₁₂ h ₁ A ₁+ρ₁₂ {dot over (h)} ₁ A₁  (1)where ρ_(w) is the density of water, ρ_(c) is the dry cement density,ρ₁₂ is the density of the slurry flowing over the weir, and A₁ is thecross-sectional area of mixing vessel 10. The parameter {dot over(m)}_(D) represents the sum of all disturbances accounting for unknownmass rate inputs into the system such as the input mass rate of air. Thederivation of Equation 1 assumes instantaneous mixing such that anychange in the relative proportions of {dot over (V)}_(w) and {dot over(V)}_(c) is instantaneously realized in the resulting value of theslurry density in mixing vessel 10. With this simplification ρ₁₂ nowrepresents the density of all the slurry in mixing vessel 10 at anygiven moment. The conservation of mass equation for mixing vessel 12 isgiven as follows:ρ₁₂ {dot over (V)} ₁₂−ρ_(s) {dot over (V)} _(s)={dot over (ρ)}_(s) h ₂ A₂+ρ_(s) {dot over (h)} ₂ A ₂  (2)where ρ_(s) is the density of the output slurry and A₂ is thecross-sectional area of mixing vessel 12. Equation 2 also assumesinstantaneous mixing such that ρ_(s) represents the density of all theslurry in mixing vessel 12 at any given moment.

The physical system can also be modeled mathematically by volumeconservation assuming that both the water and the cement added to thesystem are incompressible. This model is represented for mixing vessel10 and mixing vessel 12 by the following respective equations:{dot over (V)} _(w) +{dot over (V)} _(c) −{dot over (V)} ₁₂ +{dot over(V)} _(D) ={dot over (h)} ₁ A ₁  (3){dot over (V)} ₁₂ −{dot over (V)} _(s) ={dot over (h)} ₂ A ₂  (4)The parameter {dot over (V)}_(D) in Equation 3 represents the“volumetric disturbance flowrate,” which is herein defined as the sum ofthe flowrates of inputs, e.g., air, into the mixing process other thanthe primary materials being mixed. The term {dot over (V)}₁₂, whichrepresents the volumetric flowrate over the weir, is a non-linearfunction of the weir shape, fluid rheology and the height of fluid inmixing vessel 10. If the weir shape and the fluid rheology are assumedto be constant, {dot over (V)}₁₂ is predominantly a function of h₁ asindicated by the following equation:{dot over (V)} ₁₂ =F(h ₁)  (5)It is understood that the equations herein could also be applied toother forms of channeling the slurry from one mixing vessel to the next.Thus, Equation 5 could also define the volumetric flow rate throughother forms of channeling devices besides a weir.

FIG. 2 depicts the Laplace frequency domain state block diagram of thephysical system 34 modeled by Equations 1 through 5, which will bedescribed in more detail later. The inputs of water and dry cement tothe system are shown to come from respective supply lines 36 and 46 thatfeed a physical water valve 38 and cement valve 48. These valves 38 and48 are the control point for both slurry density and slurry flowratethrough the system. The valves 38 and 48 also represent the boundarybetween the physical system and the control process.

Flow Modulator

A procedure known as the Flow Modulator 32 is also shown in FIG. 2 thatincorporates the following Equations 6 through 13 by modulating fromcommanded volumetric flowrates to actual volumetric flow and mass ratesthrough water and cement valves 38 and 48. The positions of valves 38and 48 directly affect the rate of water and dry cement being input intothe physical system. The resulting input volumetric rate and input massrate may be represented by the following equations:{dot over (V)} _(in) ={dot over (V)} _(w) +{dot over (V)} _(c)  (6){dot over (m)} _(in)=ρ_(in) {dot over (V)} _(in)=ρ_(w) {dot over (V)}_(w)+ρ_(c) {dot over (V)} _(c)  (7)where ρ_(in) is the combined instantaneous density of both input waterand dry cement. As can be seen from Equations 6 and 7, the input rates{dot over (V)}_(w) and {dot over (V)}_(c) are directly coupled withrespect to volumetric rate and density of the slurry through the system.Designing separate control algorithms for the water valve and cementvalve could produce a system in which {dot over (V)}_(w) and {dot over(V)}_(c) are competing to control density and flowrate simultaneously,resulting in undesirable behavior. As such, {dot over (V)}_(in) and {dotover (m)}_(in) may be chosen as the decoupled control variable. Throughthese control variables the density and volumetric flowrate can becontrolled independently from each other. The desired input volumetricrate {dot over (V)}_(in) * and the desired input mass rate {dot over(m)}_(in)* can be modeled by the following equations:{dot over (m)} _(in)*={circumflex over (ρ)}_(w) {dot over (V)}_(w)*+{circumflex over (ρ)}_(c) {dot over (V)} _(c)*  (8){dot over (V)} _(in) *={dot over (V)} _(w) *+{dot over (V)} _(c)*  (9)where {dot over (V)}_(w)* and {dot over (V)}_(c)* represent the desiredcommanded rates of water and dry cement to each valve, respectively. Theparameters {circumflex over (ρ)}_(w) and {circumflex over (ρ)}_(c)represent the predetermined estimated values of water density and drycement density. Rearranging Equations 7 and 8 the commanded rates to thevalves can be represented as follows:

$\begin{matrix}{{\overset{.}{V}}_{w}^{*} = {\left( \frac{1}{{\hat{\rho}}_{c} - {\hat{\rho}}_{w}} \right)\left\lbrack {{{\hat{\rho}}_{c}{\overset{.}{V}}_{i\; n}^{*}} - {\overset{.}{m}}_{i\; n}^{*}} \right\rbrack}} & (10) \\{{\overset{.}{V}}_{c}^{*} = {\left( \frac{1}{{\hat{\rho}}_{c} - {\hat{\rho}}_{w}} \right)\left\lbrack {{\overset{.}{m}}_{i\; n}^{*} - {{\hat{\rho}}_{w}{\overset{.}{V}}_{i\; n}^{*}}} \right\rbrack}} & (11)\end{matrix}$

In order to verify that {dot over (V)}_(in) and {dot over (m)}_(in) areactually decoupled, the output rate of each valve is assumed to closelyapproximate the commanded input rate to each valve as follows:{dot over (V)}_(w)≈{dot over (V)}_(w)*  (12){dot over (V)}_(c)≈{dot over (V)}_(c)*  (13)Combining Equations 6 through 13 results in the following set ofequations:{dot over (V)}_(in)={dot over (V)}_(in)*  (14)

$\begin{matrix}{{\overset{.}{m}}_{i\; n} = {{\left( \frac{\rho_{c} - \rho_{w}}{{\hat{\rho}}_{c} - {\hat{\rho}}_{w}} \right){\overset{.}{m}}_{i\; n}^{*}} + {\left( \frac{{\rho_{w}{\hat{\rho}}_{c}} - {\rho_{c}{\hat{\rho}}_{w}}}{{\hat{\rho}}_{c} - {\hat{\rho}}_{w}} \right){\overset{.}{V}}_{i\; n}^{*}}}} & (15)\end{matrix}$Equations 14 and 15 verify that the volumetric input rate is completelyindependent of the mass input rate. Additionally, if {circumflex over(ρ)}_(c)≅ρ_(c) and {circumflex over (ρ)}_(w)≅ρ_(w), then Equation 15reduces to{dot over (m)}_(in)≅{dot over (m)}_(in)*  (16)and the mass input rate becomes independent of the volumetric inputflowrate. If the density estimations are incorrect or the valve deliveryis not approximated exactly as assumed in Equations 12 and 13, these“errors” may be absorbed into the modeled disturbance terms {dot over(V)}_(D) and {dot over (m)}_(D).

The density of the slurry mixture may be unavailable due to a lack of adensity measuring device or to the density values of the dry cement andwater being very similar (i.e., ρ_(w)≅ρ_(c)) such that density is apoorly conditioned variable for good control. A mixing system in whichthe input water rate {dot over (V)}_(w) into the first mixing vessel,the fluid height h₂ in the second mixing vessel, and the output slurryrate {dot over (V)}_(s) from the second mixing vessel are available formeasurement may be controlled using a so-called volumetric ratio mixingcontrol approach. That is, the mixing process may be controlledvolumetrically, and the chosen control variables may be the overalltotal flowrate of the slurry through the system and the percentage orratio of the slurry which is water.

In an embodiment in which the density is no longer the variable by whichthe water and the cement are proportioned, {circumflex over (ρ)}_(w) maybe set equal to 1 ({circumflex over (ρ)}_(w)=1) and {circumflex over(ρ)}_(c) may be set equal to 0 ({circumflex over (ρ)}_(c)=0). Turningback to FIG. 2, the inputs to physical system 34 now become the overallcommanded input rate {dot over (V)}_(in)* and the commanded input waterrate {dot over (V)}_(w)* into the first mixing vessel. The FlowModulator 32 may send {dot over (V)}_(w)* directly to water valve 38 viasignal 36. Further, it may send the overall commanded input rate {dotover (V)}_(in)* via signal 40 and the commanded input water rate {dotover (V)}_(w)* via signal 42 to a comparator 44 where {dot over(V)}_(w)* is subtracted from {dot over (V)}_(in)* to obtain thecommanded input cement rate {dot over (V)}_(c)*, which may then be sentto cement valve 48 via signal 46. The positions of valves 38 and 48 maybe set according to those commanded input rates.

The resulting water flowrate {dot over (V)}_(w) exiting water valve 38and the resulting cement flowrate {dot over (V)}_(c) exiting cementvalve 48 may be measured. The total input mass flowrate {dot over(m)}_(in) to the mixing process is the result of the summation(summation block 60) of the water mass flow rate {dot over (V)}_(w)(signal 50) multiplied by ρ_(w) (gain element 52) and the cement massflow rate {dot over (V)}_(c) (signal 56) multiplied by ρ_(c) (gainelement 58) as described in Equation 7.

Next, {dot over (m)}_(in) may be sent to another summation block 67 towhich the mass disturbance flowrate {dot over (m)}_(D), the total massflowrate out of the first mixing vessel, and the total mass flowratewithin the first mixing vessel also may be sent. At summation block 67,the total mass flowrate out of the first mixing vessel and the totalmass flowrate within the first mixing vessel may be subtracted from thesum of {dot over (m)}_(in) and {dot over (m)}_(D) to obtain the totalmass rate of change in the first mixing vessel. The total mass rate ofchange may then be sent via signal 72 to an Integral controllercomprising gain element 74 for multiplying the total mass rate of changeby 1/h₁A₁ to obtain the total density rate of change in the first mixingvessel. The Integral controller also comprises an integral element 76for multiplying the total density rate of change by 1/s, which is thelaplace transform representation of integration, to determine thedensity of the mixture flowing over the weir, ρ₁₂. The Integralcontroller may then feed ρ₁₂ back to summation block 67 via signals 78and 82. On its way to summation block 67, signal 78 may pass throughgain element 80 where it is multiplied by {dot over (h)}₁A₁ to obtainthe total mass flowrate in the first mixing vessel. Also, signal 80 maypass through gain element 84 where it is multiplied by {dot over (V)}₁₂to obtain the total mass flowrate out of the first mixing vessel, i.e.,over the weir. In this manner, the Integral controller may dynamicallyrecompute ρ₁₂. After being sent to integral element 76, signal 72further may be sent to gain element 86 where it is multiplied by thetotal output volumetric flowrate from the first mixing vessel {dot over(V)}₁₂ to obtain the total mass flowrate {dot over (m)}₁₂ before beingsent to yet another summation block 90.

At summation block 90, the total mass flowrate in the second mixingvessel, indicated by signal 96, and the total mass flowrate out of thesecond mixing vessel (a measured value), indicated by signal 88, may besubtracted from the {dot over (m)}₁₂ to obtain the total mass rate ofchange in the second mixing vessel. The total mass rate of change maythen be sent via signal 90 to an Integral controller comprising gainelement 92 for multiplying the total mass rate of change by 1/h₂A₂ toobtain the total density rate of change in the first mixing vessel. TheIntegral controller also comprises an integral element 94 fordetermining the density of the slurry flowing out of the second mixingvessel, ρ_(s). The Integral controller may then feed ρ_(s) back tosummation block 90 via signal 96. On its way to summation block 67,signal 96 may pass through gain element 98 where it is multiplied by{dot over (h)}₂A₂ to obtain the total mass flowrate in the second mixingvessel. In this manner, the Integral controller may dynamicallyrecompute ρ_(s).

As further shown in FIG. 2, the cement flowrate {dot over (V)}_(c)exiting cement valve 48 and the water flowrate {dot over (V)}_(w)exiting water valve 38 may be sent via signals 54 and 62, respectively,to a summation block 64 to obtain the total volumetric input flowrate{dot over (V)}_(in). Then {dot over (V)}_(in) and a total volumetricdisturbance flowrate {dot over (V)}_(D) may be sent to summation block100 via signals 65 and 102, respectively. The volumetric flowrate withinthe first mixing vessel may also be fed back to summation block 100where it is subtracted from the sum of {dot over (V)}_(in) and {dot over(V)}_(D) to obtain the total volumetric rate of change in the firstmixing vessel. The volumetric mass rate of change may then be sent viasignal 104 to an Integral controller comprising gain element 106 formultiplying the total volumetric rate of change by 1/A₁ to obtain thetotal height rate of change in the first mixing vessel. The Integralcontroller also comprises an integral element 108 for determining theheight of the mixture in the second mixing vessel, h₁. The Integralcontroller may then feed h₁ back to summation block 100 via signal 110.On its way to summation block 100, signal 110 may pass through gainelement 112 where it is multiplied by F(h₁) to obtain the totalvolumetric flowrate out of the first mixing vessel {dot over (V)}₁₂. Inthis manner, the Integral controller may dynamically recompute h₁.

Additionally, signal 104 may be sent to a gain element 114 formultiplying h₁ by F(h₁) to determine {dot over (V)}₁₂ before it is sentto yet another summation block 115. The total flowrate of the slurryexiting the second mixing vessel, {dot over (V)}_(s), is also sent viasignal 116 to summation block 115 where it is subtracted from {dot over(V)}₁₂ to obtain the total volumetric rate of change in the secondmixing vessel. The output of summation block 115 is further sent to gainelements 120 and 122 for multiplying the total volumetric rate of changeby 1/A₂ and 1/s, respectively, to thereby determine the height of theslurry in the second mixing vessel, h₂.

Volumetric Ratio Observer

The volumetric ratio of one material relative to the total materials inone of the mixing vessels may be determined using a Volumetric RatioObserver. This observer is based on the same physical dynamics describedabove and may be derived in a way that does not include densityparameters. That is, a single mixing vessel with N number of componentsbeing mixed together therein can be modeled using the law of massconservation by the following equation:ρ₁({dot over (V)} _(in))₁+ρ₂({dot over (V)} _(in))₂+ . . . +ρ_(N)({dotover (V)} _(in))_(N)−ρ_(out) {dot over (V)} _(out) +{dot over (m)}_(D)={dot over (ρ)}_(out) V _(T)+ρ_(out) {dot over (V)} _(T)  (17)where ρ_(N) is the density of the Nth component being mixed, ({dot over(V)}_(in))_(N) is the volumetric flowrate at which the Nth component isbeing added to the mixing vessel, ρ_(out) is the density of the mixtureflowing out of the mixing vessel, {dot over (V)}_(out) is the outputflowrate of the mixture from the mixing vessel, and V_(T) is the volumeof the mixture currently in the mixing vessel. The parameter {dot over(m)}_(D) represents the sum of all disturbances accounting for unknownmass rate inputs into the system and is given as follows:{dot over (m)} _(D)=ρ₁({dot over (V)} _(D))₁+ρ₂({dot over (V)} _(D))₂+ .. . +ρ_(N)({dot over (V)} _(D))_(N)  (18)where ({dot over (V)}_(D))_(N) represents the unknown volumetricflowrate disturbance of the Nth component. The total volumetric flowratedisturbance {dot over (V)}_(D) is given as the sum of all the componentdisturbances as follows:{dot over (V)} _(D)=({dot over (V)} _(D))₁+({dot over (V)} _(D))₂+ . . .+({dot over (V)} _(D))_(N)  (19)Using instantaneous mixing as described before, the density ρ_(out) maybe represented by the following equation:

$\begin{matrix}{\rho_{out} = \left( \frac{{\rho_{1}\left( V_{T} \right)}_{1} + {\rho_{2}\left( V_{T} \right)}_{2} + \ldots + {\rho_{N}\left( V_{T} \right)}_{N}}{\left( V_{T} \right)_{1} + \left( V_{T} \right)_{2} + \ldots + \left( V_{T} \right)_{N}} \right)} & (20)\end{matrix}$where (V_(T))_(N) represents the volume of the Nth component currentlyin the mixing vessel. The total volume of the mixture in the mixingvessel V_(T) may be represented by the following equation:V _(T)=(V _(T))₁+(V _(T))₂+ . . . +(V _(T))_(N)  (21)

Eliminating ρ_(out) from Equations 17 through 21 and grouping terms withcommon density coefficients, the resulting volumetric equationsdescribing the separate component flow through the mixing vessel aregiven as follows:

$\begin{matrix}\left. \begin{matrix}{{\left( {\overset{.}{V}}_{i\; n} \right)_{1} - {\left( \frac{\left( V_{T} \right)_{1}}{V_{T}} \right){\overset{.}{V}}_{out}} + \left( {\overset{.}{V}}_{D} \right)_{1}} = \left( {\overset{.}{V}}_{T} \right)_{1}} \\{{\left( {\overset{.}{V}}_{i\; n} \right)_{2} - {\left( \frac{\left( V_{T} \right)_{2}}{V_{T}} \right){\overset{.}{V}}_{out}} + \left( {\overset{.}{V}}_{D} \right)_{2}} = \left( {\overset{.}{V}}_{T} \right)_{2}} \\\vdots \\{{\left( {\overset{.}{V}}_{i\; n} \right)_{N} - {\left( \frac{\left( V_{T} \right)_{N}}{V_{T}} \right){\overset{.}{V}}_{out}} + \left( {\overset{.}{V}}_{D} \right)_{N}} = \left( {\overset{.}{V}}_{T} \right)_{N}}\end{matrix} \right\} & (22)\end{matrix}$Here the volumetric ratio of the Nth component with respect to theoverall volume of the mixture is given as

$\begin{matrix}{\left( R_{out} \right)_{N} = \left( \frac{\left( V_{T} \right)_{N}}{V_{T}} \right)} & (23)\end{matrix}$where the notation (R_(out))_(N) incorporates the instantaneous mixingassumption, indicating not only the volumetric ratio of the Nthcomponent to the total materials in the mixing vessel but also thevolumetric flowrate ratio of the Nth component to the total outputflowrate {dot over (V)}_(out). Combining Equations 21 and 23 gives therelationship between all the component volumetric ratios as follows:(R _(out))₁+(R _(out))₂+ . . . +(R _(out))_(N)=1  (24)

The state block diagrams of the primary components of Volumetric RatioObservers (VRO's) for a single mixing vessel and for two mixing vesselsare shown in FIG. 3A and FIG. 3B, respectively. Using the same notationfrom earlier, the symbol (^) indicates that a parameter has beenestimated. The commanded or setpoint inputs for the VRO's represent thecommanded rates to the actual physical system and are signified by thesymbol (*). The VRO may be implemented using various arrangements ofclosed loops, as will be detailed later in particular embodiments of theVolumetric Mixing Control approach. The VRO may serve to decouple theeffects of disturbances on the system.

As shown in FIG. 3A, the VRO for the Nth component being fed to a singlemixing vessel may include a summation block 55 for subtracting anestimated output flowrate of the Nth component ({dot over ({circumflexover (V)}_(out))_(N) from the sum of a volumetric disturbance flowrateof the Nth component, ({dot over ({circumflex over (V)}_(D))_(N), and acommanded input flowrate of the Nth component ({dot over(V)}_(in)*)_(N). The ({dot over ({circumflex over (V)}_(out))_(N) may befed to summation block 55 via signal 65, the ({dot over ({circumflexover (V)}_(D))_(N) may be fed to summation block 55 via signal 51, andthe ({dot over (V)}_(in)*)_(N) may be fed to summation block 55 viasignal 53. The output of summation block 55, as indicated by signal 57,may represent an estimated volumetric rate of change of the Nthcomponent in the mixing vessel. The estimated volumetric rate of changeof the Nth component may be fed to an Integral controller comprising anintegral element 59 for computing the estimated volume of the Nthcomponent in the mixing vessel. The Integral controller may also includea gain element 61 for multiplying the estimated volume of the Nthcomponent in the mixing vessel by 1/(the estimated volume of the totalmaterials in the mixing vessel) to obtain the estimated output ratio ofthe Nth component to the total materials in the mixing vessel,({circumflex over (R)}_(out))_(N). It may further include gain element63 for multiplying ({circumflex over (R)}_(out))_(N) by the totalestimated output flowrate from the mixing vessel, {dot over (V)}_(out),to estimate the output flowrate of the Nth component ({dot over({circumflex over (V)}_(out))_(N), which may be negatively fed back tosummation block 55. Thus, the Integral controller dynamically recomputes({dot over ({circumflex over (V)}_(out))_(N).

As illustrated in FIG. 3B, the Volumetric Ratio Observer may be expandedto cover two mixing vessels. In this embodiment, the term ({dot over({circumflex over (V)}₁₂)_(N) is the estimated flowrate of the Nthcomponent out of the first mixing vessel and into the second mixingvessel. The total estimated flowrate between the two mixing vessels,i.e., over the weir, may be represented by{dot over ({circumflex over (V)} ₁₂=({dot over ({circumflex over (V)}₁₂)₁+({dot over ({circumflex over (V)} ₁₂)₂+ . . . +({dot over({circumflex over (V)} ₁₂)_(N)  (25)The volumes of the mixture in the first mixing vessel and the secondmixing vessel are given by {circumflex over (V)}₁ and {circumflex over(V)}₂, respectively. The portion of the state block diagram depicted inFIG. 3B that dynamically recomputes ({dot over ({circumflex over(V)}₁₂)_(N) using a first Integral controller is the same as the stateblock diagram shown in FIG. 3A with the exception that gain element 61multiplies by 1/{circumflex over (V)}₁ and gain element 63 multiplies by{dot over ({circumflex over (V)}₁₂. The ({dot over ({circumflex over(V)}₁₂)_(N) computed by the first Integral controller may be sent to asummation block 67 via signal 79 where an estimated value of the outputflowrate ({dot over ({circumflex over (V)}_(out))_(N) from the secondmixing vessel is subtracted from ({dot over ({circumflex over(V)}₁₂)_(N) to obtain the volumetric rate of change in the second mixingvessel. This volumetric rate of change is then sent to a second Integralcontroller via signal 69. The second Integral controller comprises anintegral element 71 for determining the total volume of the Nthcomponent in the second mixing vessel, ({circumflex over (V)}₂)_(N). Italso comprises gain element 73 for multiplying ({circumflex over(V)}₂)_(N) by 1/{circumflex over (V)}₂ to determine ({circumflex over(R)}_(out))_(N) and gain element 75 for multiplying ({circumflex over(R)}_(out))_(N) by {dot over (V)}_(out), thereby determining theestimated output flowrate of the Nth component from the second mixingvessel, ({dot over ({circumflex over (V)}_(out))_(N). The ({dot over({circumflex over (V)}_(out))_(N) may then be negatively fed back tosummation block 67 via signal 77 such that it may be dynamicallyrecomputed. It is understood that the VRO is not limited to one or twomixing vessels but may be used for any number of mixing vessels by theaddition of an Integral controller for each additional mixing vessel.Further, control schemes like those shown in FIGS. 3A and 3B may beimplemented for any component being mixed in the one or more mixingvessels. There is no limit to the number of components that may be mixedtogether using the control system described herein.Cement Mixing Control Scheme

FIG. 4 illustrates one embodiment of the volumetric ratio mixing controlscheme mentioned earlier. The process being controlled comprises mixingcement and water together in a mixing apparatus containing two mixingvessels separated by a weir as shown in FIG. 1. FIG. 4 depicts a controlsystem 130 that includes two Height Observers 132 and 134, a StateFeedback Controller 136, a Flow Regulator 138, and a Volumetric RatioObserver 140. The Flow Modulator 32 and the state block diagram of thephysical system 34 that are depicted in FIG. 2 are also shown in FIG. 4.A detailed description of these parts of the control scheme may be foundin the previous discussion of FIG. 2.

The first Height Observer 132 depicted in FIG. 4 takes as input themeasured height h₂ of fluid in the second mixing vessel, the measuredoutput flowrate of the slurry {dot over (V)}_(s) exiting the secondmixing vessel, and the overall commanded volumetric input flowrate {dotover (V)}_(in)*. This Height Observer 132 then estimates the fluidheight in the second mixing vessel, which is used as feedback in State.Feedback Controller 136. It further estimates the overall volumetricdisturbance flowrate {dot over ({circumflex over (V)}_(D), which is usedfor disturbance input decoupling in Flow Regulator 138. The secondHeight Observer 134 depicted in FIG. 4, also known as the Weir FlowObserver, takes as input h₂ and {dot over (V)}_(s). With only these twoinputs, Height Observer 134 estimates the flowrate of the fluid {dotover ({circumflex over (V)}₁₂ flowing over the weir from the firstmixing vessel to the second mixing vessel.

Describing Height Observer 132 in more detail, h₂ may be fed fromphysical system 34 to a summation block 146 via signal 142. Theestimated height of the fluid ĥ₂ in the second mixing vessel may also besent via signal 144 to summation block 146 where it is subtracted fromh₂ to determine an estimation of a height error for the second mixingvessel. This estimation of height error may then be fed via signal 148to a Proportional-Integral controller 152 comprising an integral element154, an integral gain element 156 for multiplying it by a constantN_(io1), and a proportional gain element 150 for multiplying it by aconstant N_(o1). The PI gains may be set to remove the noise andoscillations of the second mixing vessel from the height estimation. Theoutput of integral gain element 156 and of proportional gain element 150may then be summed at a summation block 158 to estimate the totalvolumetric disturbance flowrate {dot over ({circumflex over (V)}_(D).The {dot over ({circumflex over (V)}_(D) may be sent via signal 160 toanother summation block 166. In addition, both the {dot over (V)}_(in)*and the {dot over (V)}_(s) as measured by a sensor may be fed tosummation block 166 via signals 162 and 164, respectively. At summationblock 166, the {dot over (V)}_(s) may be subtracted from the sum of {dotover (V)}_(in)* and {dot over ({circumflex over (V)}_(D) to obtain thevolumetric rate of change in the second mixing vessel. The output ofsummation block 166 may be sent to an Integral controller comprising amultiplier block gain element 170 where it is multiplied by 1/(theestimated cross-sectional area of the second mixing vessel) to convertthe volumetric rate of change to the rate of height change in the secondmixing vessel. This rate of height change may be sent to an integralelement 172 to compute ĥ₂. The Height Observer 132 may continue todynamically recompute ĥ₂ in this manner.

As shown in FIG. 4, the Weir Flow Observer 134 may be very similar tothe Height Observer 132. That is, it may also include a summation block178 to which h₂ is fed via signal 142 and ĥ₂ is negatively fed viasignal 176. The output of summation block 178, i.e., an estimation of aheight error for the second mixing vessel, may then be fed via signal148 to a Proportional-Integral controller 184 comprising an integralelement 186, an integral gain element 188 for multiplying it by aconstant N_(io2), and a proportional gain element 182 for multiplying itby a constant N_(o2). The output of integral gain element 188 and ofproportional gain element 182 may then be summed at a summation block190 to estimate the total output flowrate {dot over ({circumflex over(V)}₁₂ from the first mixing vessel. The {dot over ({circumflex over(V)}₁₂ may then be sent via signal 192 to another summation block 194 towhich the {dot over (V)}_(s) may also be sent via signal 195. Atsummation block 166, the {dot over (V)}_(s) may be subtracted from the{dot over ({circumflex over (V)}₁₂ to obtain the volumetric rate ofchange in the second mixing vessel. The output of summation block 194may be sent to an Integral controller comprising a gain element 198where it is multiplied by 1/(the estimated cross-sectional area of thesecond mixing vessel) to convert the volumetric rate of change to therate of height change in the second mixing vessel. This rate of heightchange may be sent to an integral element 200 to compute ĥ₂. The HeightObserver 134 may continue to dynamically recompute ĥ₂ in this manner.Additional information related to height observers may be found in U.S.patent application Ser. No. 11/029,072, entitled “Methods And Systemsfor Estimating a Nominal Height or Quantity of a Fluid in a Mixing TankWhile Reducing Noise,” filed on Jan. 4, 2005, which is incorporated byreference herein in its entirety.

In order to maintain enough fluid in the physical system to supply adesired output flowrate of the slurry {dot over (V)}_(s)* from thesecond mixing vessel, a State Feedback Controller 136 may be implementedwhere ĥ₂ is the state feedback. In particular, the ĥ₂ determined byHeight Observer 132 may be sent via signal 204 to a summation block 206where it is subtracted from the commanded height of the fluid h₂* in thesecond mixing vessel, indicated by signal 202, to estimate the heighterror for the second mixing vessel. The output of summation block 206may be sent to a proportional gain element 210 via signal 216 where itis multiplied by the constant N_(p) before being summed with {dot over(V)}_(s)* at summation block 214. In this manner, State FeedbackController 136 computes a commanded output flowrate {dot over (V)}₁₂* ofthe total materials from the first mixing vessel. This desired outputflowrate is then sent through Flow Regulator 138 and Flow Modulator 32to adjust the water and cement valves as needed.

This implementation of Height Observer 132 and Weir Flow

Observer 134 with full state feedback allows control system 130 to befully enhanced. These height observers not only provide filtered,zero-lag estimations of the actual signals but also provide fordisturbance estimation.

The estimated output flowrate {dot over ({circumflex over (V)}₁₂ fromthe first mixing vessel determined by Weir Flow Observer 134 may be fedback to an upper portion of Flow Regulator 138 to “cancel” or decouplethe negative state feedback that naturally occurs in the physicalsystem. The estimated total volumetric disturbance flowrate {dot over({circumflex over (V)}_(D) determined by Height Observer 132 resultsfrom input air and errors between commanded volumetric rates and actualvolumetric rates through the valves. This volumetric disturbanceflowrate estimation may be negatively fed back to Flow Regulator 138 todecouple the effect of the disturbance in the system, thereby making thecontrol system invariant to unmeasured volumetric flowrate disturbances.

Describing Flow Regulator 138 in more detail, {dot over ({circumflexover (V)}₁₂ may be fed back to summation block 220 where it issubtracted from {dot over (V)}₁₂*, which is fed to summation block 220via signal 216. The output of summation block 220 may then be sent to aproportional gain element 224 where it may be multiplied by a constantK_(v) before being sent to another summation block 230. The {dot over({circumflex over (V)}_(D) may be fed back to summation block 230 viasignal 226, and {dot over ({circumflex over (V)}₁₂ may also be fed tosummation block 230 via signal 228 such that {dot over ({circumflex over(V)}_(D) is subtracted from the sum of the output of gain element 224and {dot over ({circumflex over (V)}₁₂. The output of summation block230 is the total commanded input flowrate {dot over (V)}_(in)* to themixing process, which may be fed to Flow Modulator 32 via signal 232. Asdescribed previously, Flow Modulator 32 may modulate from the commandedflowrate {dot over (V)}_(in)* to the actual input flowrate {dot over(V)}_(in).

The Volumetric Ratio Observer 140 shown in FIG. 4 may be implemented toestimate the ratio of water to total materials in the first mixingvessel in accordance with the following equation:

$\begin{matrix}{\left( {\hat{R}}_{12} \right)_{w} = \left( \frac{\left( {\hat{V}}_{1} \right)_{w}}{{\hat{V}}_{1}} \right)} & (26)\end{matrix}$The inputs to Volumetric Ratio Observer 140 may include the commandedinput water rate {dot over (V)}_(w)* and the measured input water rate{dot over (V)}_(w) as well as the closed loop estimate of the volumetricdisturbance {dot over ({circumflex over (V)}_(D) from Height Observer132. The measured and commanded input water rates may be used toestimate the input disturbance flowrate ({dot over ({circumflex over(V)}_(D))_(w) in the water delivery. This disturbance may be used fordisturbance input decoupling within Flow Regulator 138 and to determinethe input disturbance flowrate ({dot over ({circumflex over(V)}_(D))_(c) in the cement delivery within Volumetric Ratio Observer140.

In the embodiment of Volumetric Ratio Observer 140 shown in FIG. 4, asummation block 240 is employed to determine the estimated volumetricdisturbance flowrate of the water ({dot over ({circumflex over(V)}_(D))_(w) by comparing {dot over (V)}_(w) to {dot over (V)}_(w)*,which are fed to summation block 240 via signals 236 and 238,respectively. The ({dot over ({circumflex over (V)}_(D))_(w) may then befed to a summation block 266 to which {dot over (V)}_(w)* is also fedvia signal 262. Further, an estimated output flowrate of the water ({dotover ({circumflex over (V)}₁₂)_(w) from the first mixing vessel may benegatively fed to summation block 266. At summation block 266, the ({dotover ({circumflex over (V)}₁₂)_(w) may be subtracted from the summationof ({dot over ({circumflex over (V)}_(D))_(w) and {dot over (V)}_(w)* todetermine an estimated volumetric rate of change of the water in thefirst mixing vessel. The output of summation block 266 may be fed viasignal 268 to an Integral controller comprising an Integral element 270and a gain element 272 for multiplying it by 1/{circumflex over (V)}₁,thereby determining the estimated volumetric ratio ({circumflex over(R)}₁₂)_(w) of the water to the total materials in the first mixingvessel. The Integral Controller further comprises another gain element274 for multiplying ({circumflex over (R)}₁₂)_(w) by the total estimatedoutput flowrate {dot over ({circumflex over (V)}₁₂ from the first mixingvessel to estimate the output flowrate of the water ({dot over({circumflex over (V)}₁₂)_(w) from the first mixing vessel. Thisestimated output flowrate of the water ({dot over ({circumflex over(V)}₁₂)_(w) may then be fed back to summation block 266 via signal 264.The Integral controller continues to dynamically recompute the estimatedrate ({dot over ({circumflex over (V)}₁₂)_(w) in this manner.

The Volumetric Ratio Observer 140 may also determine the volumetricdisturbance flowrate of the cement ({dot over ({circumflex over(V)}_(D))_(c) through the use of another summation block 244 forsubtracting the volumetric disturbance flowrate of the water ({dot over({circumflex over (V)}_(D))_(w) from the total input volumetricdisturbance flowrate {dot over ({circumflex over (V)}_(D) determined byHeight Observer 132. The ({dot over ({circumflex over (V)}_(D))_(w) maybe fed from the output of summation block 240 to summation block 244 viasignal 242, and the {dot over ({circumflex over (V)}_(D) may be fed tosummation block 234 via signal 234. The volumetric disturbance flowrateof the cement ({dot over ({circumflex over (V)}_(D))_(c) may then besent to yet another summation block 252 via signal 246. Further, acommanded input cement flowrate {dot over (V)}_(c)* and an estimatedoutput flowrate of the cement ({dot over ({circumflex over (V)}₁₂)_(c)from the first mixing vessel may be fed to summation block 252 viasignals 248 and 250, respectively. At summation block 252, the ({dotover ({circumflex over (V)}₁₂)_(c) may be subtracted from the summationof ({dot over ({circumflex over (V)}_(D))_(c) and {dot over (V)}_(c)* todetermine an estimated volumetric rate of change of the cement in thefirst mixing vessel. The output of summation block 252 may be fed viasignal 254 to an Integral controller comprising an integral element 256,a gain element 258 for multiplying it by 1/{circumflex over (V)}₁, andanother gain element 260 for multiplying it by the total estimatedoutput flowrate {dot over ({circumflex over (V)}₁₂ from the first mixingvessel. As a result, the estimated volumetric rate of change of thecement in the first mixing vessel may be converted to the estimatedoutput flowrate of the cement ({dot over ({circumflex over (V)}₁₂)_(c)from the first mixing vessel. This estimated output flowrate of thecement ({dot over ({circumflex over (V)}₁₂)_(c) may then be fed back tosummation block 252 via signal 250. The Integral controller continues todynamically recompute the estimated rate ({dot over ({circumflex over(V)}₁₂)_(c) in this manner.

The estimated water ratio ({circumflex over (R)}₁₂)_(w) in the firstmixing vessel may be fed back and compared to the desired water ratio(R₁₂*)_(w) in a Proportional controller within a lower portion of FlowRegulator 138. That is, the ({circumflex over (R)}₁₂)_(w) may be fed viasignal 278 from Volumetric Ratio Observer 140 to a summation block 279of Flow Regulator. Further, the (R₁₂*)_(w) may be fed via signal 276 tosummation block 279. The output of summation block 279 may then be fedvia signal 280 to a proportional gain element 282 for multiplying it byK_(m) before being sent to a summation block 288 of Flow Regulator 138.The estimated output flowrate of the water ({dot over ({circumflex over(V)}₁₂)_(w) exiting the first mixing vessel also may be fed back to theFlow Regulator for decoupling purposes. That is, the ({dot over({circumflex over (V)}₁₂)_(w) may be fed via signal 286 to summationblock 288. Further, the estimated volumetric disturbance flowrate of thewater ({dot over ({circumflex over (V)}_(D))_(w) may be fed to summationblock 288. At summation block 288, the ({dot over ({circumflex over(V)}_(D))_(w) may be subtracted from the summation of the output of gainelement 282 and ({dot over ({circumflex over (V)}₁₂)_(w), therebycomputing the commanded input flowrate of the water {dot over (V)}_(w)*.The {dot over (V)}_(w)* may be fed to Flow Modulator 32 via signal 290.As described previously, Flow Modulator 32 may modulate from the totalcommanded input volumetric flowrate {dot over (V)}_(in)* and thecommanded input volumetric flow rate of the water {dot over (V)}_(w)* tothe actual total input mass flowrate {dot over (m)}_(in). (See FIG. 2).

The foregoing implementation Volumetric Ratio Observer 140 with statefeedback allows control system 130 to be fully enhanced. The VROprovides for filtered, zero-lag estimations of actual signals.

FIG. 5 illustrates another embodiment of the volumetric ratio mixingcontrol scheme in which the process being controlled comprises mixingcement and water together in a mixing apparatus containing two mixingvessels separated by a weir as shown in FIG. 1. FIG. 5 depicts a controlsystem 291 that is the same as control system 130 of FIG. 4 except forsome changes in the Volumetric Ratio Observer, the State FeedbackController, and the Flow Regulator. In particular, this embodimentextends the VRO in FIG. 4 from a one vessel implementation to a twovessel implementation for estimating the ratio of water to totalmaterials in the second mixing vessel rather than the first mixingvessel. This embodiment also provides for water ratio control within theState Feedback Controller.

The differences of FIG. 5 are described in more detail below, beginningwith Volumetric Ratio Observer 141. In particular, the estimated outputflowrate of the water ({dot over ({circumflex over (V)}₁₂)_(w) from thefirst mixing vessel may be further passed to another summation block292. At summation block 292, an estimated output flowrate of the water({dot over ({circumflex over (V)}_(s))_(w) from the second mixing vesselmay be subtracted from ({dot over ({circumflex over (V)}₁₂)_(w) todetermine the volumetric rate of change in the second mixing vessel. Theoutput of summation block 292 may then be sent via signal 294 to anIntegral controller comprising an integral element 296 and a gainelement 298 for multiplying it by 1/{circumflex over (V)}₂ to determinethe estimated volumetric ratio of the water to total materials{circumflex over (R)}_(w) in the second mixing vessel. The Integralcontroller may further include a gain element 300 for multiplying{circumflex over (R)}_(w) by the total output flowrate {dot over(V)}_(s) from the second mixing vessel, which may be measured, todetermine the estimated total output flowrate ({dot over ({circumflexover (V)}_(s))_(w) of the water. The ({dot over ({circumflex over(V)}_(s))_(w) may be fed back to summation block 292 via signal 302,allowing it to be dynamically recomputed.

Another difference between Volumetric Ratio Observer 141 and VolumetricRatio Observer 140 is that the estimated output flowrate of the cement({dot over ({circumflex over (V)}₁₂)_(c) from the second mixing vesselmay be further passed to another summation block 303. At summation block303, an estimated output flowrate of the cement ({dot over ({circumflexover (V)}_(s))_(c) from the second mixing vessel may be subtracted from({dot over ({circumflex over (V)}₁₂)_(c) to determine the volumetricrate of change in the second mixing vessel. The output of summationblock 303 may then be sent via signal 304 to an Integral controllercomprising an integral element 306 and a gain element 308 formultiplying it by 1/{circumflex over (V)}₂ to determine the estimatedvolumetric ratio of the cement to total materials {circumflex over(R)}_(c) in the second mixing vessel. The Integral controller mayfurther include a gain element 310 for multiplying {circumflex over(R)}_(c) by the total output flowrate {dot over (V)}_(s) from the secondmixing vessel, which may be measured, to determine the estimated totaloutput flowrate ({dot over ({circumflex over (V)}_(s))_(c) of thecement. Further, the ({dot over ({circumflex over (V)}_(s))_(c) may befed back to summation block 303 via signal 312, allowing it to bedynamically recomputed.

In this embodiment, State Feedback Controller 137 may be different inthat it may engage in proportional control of the volumetric ratio ofthe water to the total materials in the second mixing vessel, comparingthe desired water ratio R_(w)* to the estimated water ratio {circumflexover (R)}_(w) determined by Volumetric Ratio Observer 141. The{circumflex over (R)}_(w) may be calculated using the followingequation:

$\begin{matrix}{{\hat{R}}_{w} = \left( \frac{\left( {\hat{V}}_{2} \right)_{w}}{{\hat{V}}_{2}} \right)} & (27)\end{matrix}$Describing State Feedback Controller 137 in more detail, the {circumflexover (R)}_(w) and the R_(w)* may be fed to summation block 318 viasignals 314 and 316 respectively. The output of summation block 318 maybe fed to a proportional gain element 322 for multiplying it by aconstant K_(p) and a gain element 324 for multiplying it by the desiredtotal output flowrate {dot over (V)}₁₂* from the first mixing vesselbefore being positively sent to a summation block 330. The R_(w)* mayalso pass through a gain element 328 for multiplying it by the totaldesired output flowrate of the slurry {dot over (V)}_(s)* exiting thesecond mixing vessel to determine the desired output flowrate of thewater exiting the second vessel. This desired output flowrate of thewater may be positively fed forward to summation block 330 via signal326 to decouple the effect of the water exiting the second mixingvessel.

The output of State Feedback Controller 137 and the estimated flowrateof water ({dot over ({circumflex over (V)}₁₂)_(w) out of the firstmixing vessel, as determined by Volumetric Ratio Observer 141, may befed via respective signals 276 and 278 to a summation block 279 of FlowRegulator 139 where they may be compared. The Flow Regulator 193 isimplemented in the same way as Flow Regulator 138 in FIG. 4 with theexception that the proportional control compares the estimated flowrateof water ({dot over ({circumflex over (V)}₁₂)_(w) out of the firstmixing vessel with the commanded flowrate of water ({dot over(V)}₁₂)_(w) from State Feedback Controller 137. In particular, theoutput of summation block 279 may be sent via signal 280 to aproportional gain element 282 for multiplying it by a constant K_(m)before sending it to another summation block 288, where the estimatedvolumetric disturbance flowrate of the water ({dot over ({circumflexover (V)}_(D))_(w) may be subtracted from it and from the estimatedoutput flowrate of the water ({dot over ({circumflex over (V)}₁₂)_(w)from the first mixing vessel. The ({dot over ({circumflex over(V)}_(D))_(w) determined by Volumetric Ratio Observer 141 may be sent tosummation block 288 via signal 284. Further, the estimated outputflowrate of the water ({dot over ({circumflex over (V)}₁₂)_(w) from thefirst mixing vessel may be sent to summation block 288. The output ofsummation block 288 may be the commanded input water flowrate {dot over(V)}_(w)*, which may be fed to Flow Modulator 32.

FIG. 6 depicts yet another embodiment of the volumetric ratio mixingcontrol scheme in which the process being controlled comprises mixingcement and water together in a mixing apparatus containing two mixingvessels separated by a weir as shown in FIG. 1. FIG. 6 depicts a controlsystem 331 that is similar to control system 130 of FIG. 4. Notably,control system 331 does not contain a Weir Flow Observer. Further, thisembodiment extends the VRO in FIG. 4 from a one vessel implementation toa two vessel implementation for estimating the ratio of water to totalmaterials in the second mixing vessel rather than the first mixingvessel. This two vessel VRO may also be used to estimate the totalvolumetric disturbance flowrate by applying an internal PI controller tothe fluid height in the second mixing vessel. Moreover, within the VROthe commanded total volumetric flowrate {dot over (V)}₁₂* out of thefirst mixing vessel may be used as an estimate of the actual flowrateout of the first mixing vessel to determine the state feedbackdecoupling term for the Flow Regulator.

In this embodiment, a PI control loop may act directly on the watervalve within the Flow Modulator using the actual measured input waterflowrate as feedback (not shown). Tuned for a faster response time thanthe rest of the system, the water valve thus may be driven to producethe desired input water flowrate, resulting in zero steady state error.Therefore, an assumption may be made that all resulting volumetricdisturbances are a result of errors in the cement valve between thecommanded input cement flowrate and the actual delivered input cementflowrate (({dot over ({circumflex over (V)}_(D))_(w)=0; {dot over({circumflex over (V)}_(D)=({dot over ({circumflex over (V)}_(D))_(c)).As mentioned earlier, the VRO may determine this disturbance by closinga loop on the estimated height of fluid in the second mixing vessel. Theestimated height of fluid ĥ₂ in the second mixing vessel may be found byassuming the estimated cross-sectional area Â₂ of the second mixingvessel is known for a given volume of fluid in the vessel.

Since the estimated volumetric disturbance term {dot over ({circumflexover (V)}_(D) is assumed to only contain errors due to the cement valve,it is only fed back into the upper portion of the Flow Regulator. Whenfed through the Flow Modulator this only makes adjustments to the cementcommand. In summary, valve errors in both valves are decoupled by thecombined effects of the PI control on the water valve and thedisturbance input decoupling on the cement valve.

The differences between control system 331 in FIG. 6 and control system130 in FIG. 4 are described in more detail below. The volumetricdisturbance flowrate of the cement being fed to summation block 248 viasignal 246 may be determined by first feeding the height of the fluid h₂in the second mixing vessel to summation block 330 via signal 320. Atsummation block 330, the sum of the estimated height of the water(ĥ₂)_(w) and the estimated height of the cement (ĥ₂)_(c) in the secondmixing vessel may be subtracted from h₂, thereby estimating the heighterror for the second mixing vessel. This height error may be sent to aPI controller 332 via signal 338. The PI controller may comprise anintegral element 334, an integral gain element 336 for multiplying theheight error by N_(io1), and a proportional gain element 340 formultiplying it by N_(o1) before sending it to summation block 342. Theoutput of summation block 342 is the estimated volumetric disturbanceflowrate of the cement, which is equivalent to the estimated totalvolumetric disturbance flowrate {dot over ({circumflex over (V)}_(D) asrepresented by signal 344. Also, no estimated volumetric disturbanceflowrate of the water is fed to summation block 266 nor to summationblock 288 of Flow Regulator 143 since this estimated rate is equivalentto zero.

Additionally, in Volumetric Ratio Observer 145, respective gain elements274 and 260 may be replaced by respective gain elements 275 and 261,which may multiply the respective estimated ratios of the water and thecement in the first mixing vessel by the commanded total output flowrate{dot over (V)}₁₂* from the first mixing vessel. Moreover, the estimatedoutput flowrate of the water ({dot over ({circumflex over (V)}₁₂)_(w)from the first mixing vessel may be further passed to another summationblock 292. At summation block 292, an estimated output flowrate of thewater ({dot over ({circumflex over (V)}_(s))_(w) from the second mixingvessel may be subtracted from ({dot over ({circumflex over (V)}₁₂)_(w)to determine the volumetric rate of change in the second mixing vessel.The output of summation block 292 may then be sent via signal 294 to anIntegral controller comprising an integral element 296 and a gainelement 299 for multiplying it by 1/Â₂ to determine the estimated heightof the water (ĥ₂)_(w) in the second mixing vessel. The Integralcontroller may further include a gain element 301 for multiplying(ĥ₂)_(w) by 1/h₂ and a gain element 300 for multiplying (ĥ₂)_(w) by themeasured total output flowrate {dot over (V)}_(s) from the second mixingvessel to determine the estimated total output flowrate ({dot over({circumflex over (V)}_(s))_(w) of the water. The ({dot over({circumflex over (V)}_(s))_(w) may be fed back to summation block 292via signal 302, allowing it to be dynamically recomputed.

Another difference between Volumetric Ratio Observer 145 and VolumetricRatio Observer 140 is that the estimated output flowrate of the cement({dot over ({circumflex over (V)}₁₂)_(c) from the second mixing vesselmay be further passed to another summation block 303. At summation block303, an estimated output flowrate of the cement ({dot over ({circumflexover (V)}_(s))_(c) from the second mixing vessel may be subtracted from({dot over ({circumflex over (V)}₁₂)_(c) to determine the volumetricrate of change in the second mixing vessel. The output of summationblock 303 may then be sent via signal 304 to an Integral controllercomprising an integral element 306 and a gain element 309 formultiplying it by 1/Â₂ to determine the estimated height of the cement(ĥ₂)_(w) in the second mixing vessel. The Integral controller mayfurther include a gain element 311 for multiplying (ĥ₂)_(c) by 1/h₂ anda gain element 310 for multiplying (ĥ₂)_(c) by the measured total outputflowrate {dot over (V)}_(s) from the second mixing vessel to determinethe estimated total output flowrate ({dot over ({circumflex over(V)}_(s))_(c) of the water. Further, the ({dot over ({circumflex over(V)}_(s))_(c) may be fed back to summation block 303 via signal 312,allowing it to be dynamically recomputed. The (ĥ₂)_(w) and (ĥ₂)_(c) maybe fed to and added together at summation block 326 before being fed tosummation block 330 via signal 328.

In addition, the total estimated volumetric disturbance flowrate {dotover ({circumflex over (V)}_(D) determined by Volumetric Ratio Observer145 may be negatively fed to a summation block 230 of Flow Regulator143, which does not contain a proportional controller for the volumetricflowrate exiting the first mixing vessel as in FIG. 4. Instead, the {dotover ({circumflex over (V)}_(D) may be subtracted from the commandedtotal output flowrate {dot over (V)}₁₂* from the first mixing vessel,which may be fed to summation block 230 via signal 216. As in FIG. 4,the output of summation block 230 is the total commanded input flowrate{dot over (V)}_(in)*. FIG. 6 also depicts {dot over (V)}_(in)* being fedvia signal 162 from Flow Regulator 143 to summation block 166 of HeightObserver 132.

FIG. 11 shows yet another embodiment, with a different implementation ofthe disclosed volumetric control ideas. Note the following two aspectsof this embodiment:

-   -   1) Variable height control: The height setpoint is changed        depending on the height observer error, or cement rate error.        This is done to reduce effects of water/cement ratio problems if        we have flow inconsistencies in the cement supply system. This        normally occurs when we switch between cement supply bins or        pods.    -   2) Ideal ratio control: Instead of a ratio observer outlined in        the previous embodiments this system uses the idea case by only        inputting the output flow rate and assuming all other values.

For a mixing system in which the measured parameters include the inputwater flowrate {dot over (V)}_(w) into the first mixing vessel, theslurry density ρ₁₂ in the first mixing vessel, the fluid height h₂ inthe second mixing vessel, and the output slurry flowrate {dot over(V)}_(s) from the second mixing vessel, any of the embodiments discussedpreviously may be employed to control the system. However, one of theinherent problems with the mixing system depicted in FIG. 1 is theintroduction of air into the mixture. Air entrained in the mixture maycause the overall slurry volume in the mixing vessels to be larger thanexpected, resulting in an increased h₂ value. Additionally, airentrained in the mixture may cause the measured density of the mixtureto be lower than expected. For most applications it is ideal to be ableto mix the water and the cement to a density and a volume that does notreflect the entrainment of air. Fortunately, for a system that includesfour sensors for the four measured parameters mentioned above, theVolumetric Ratio Observer may be implemented to predict the ratio of notonly the water and cement in the mixture but also the amount of airentrained therein. As such, the system can be controlled to mix exactlythe desired proportions of water and cement.

FIG. 7 illustrates an embodiment of the primary components of a twovessel Volumetric Ratio Observer 350 for modeling a system in whichthree components, i.e., water, cement, and air, are mixed through thesystem. The Volumetric Ratio Observer 350 includes control schemes 352,354, and 356 for the water, the cement, and the air, respectively. Thosecontrol schemes are very similar to the control scheme shown in FIG. 3Bexcept that the gain element for multiplying 1/s by the estimated totaloutput flowrate {dot over ({circumflex over (V)}₁₂ from the first mixingvessel is replaced by a gain element for multiplying 1/s by a commandedtotal output flowrate from the first mixing vessel {dot over (V)}₁₂*. Inthis embodiment, the commanded input water flowrate {dot over (V)}_(w)*and the measured input water flowrate {dot over (V)}_(w) are also known,allowing the disturbance in water flowrate to be calculated directly.That is, the {dot over (V)}_(w) and the {dot over (V)}_(w)* may be fedvia respective signals 364 and 366 to a summation block 368 forcomparing the two and thus determining the estimated volumetricdisturbance flowrate of the water ({dot over ({circumflex over(V)}_(D))_(w).

Disturbances due to the cement delivery and due to the entrained air maybe provided from external observer controllers that may be implementedvia hardware or software modules. The total mass disturbance flowrate{dot over ({circumflex over (m)}_(D) may be estimated by a DensityObserver and the total volumetric disturbance flowrate {dot over({circumflex over (V)}_(D) may be estimated by a Height Observer asdescribed previously. Suitable density observers are described in U.S.patent application Ser. No. 11/121,278, filed on May 3, 2005. Using theestimated parameter values of water density and cement density, thesedisturbances may be converted into the estimated volumetric flowratedisturbance ({dot over ({circumflex over (V)}_(D))_(c) of the cement andthe estimated disturbance due to the volumetric flowrate of entrainedair ({dot over ({circumflex over (V)}_(D))_(a). An assumption is madethat the density of air is relatively insignificant (ρ_(a)≅0) comparedto the density of water and cement.

More specifically, the ({dot over ({circumflex over (V)}_(D))_(w)computed by summation block 368 may be multiplied by the estimateddensity of water by passing it to a gain element 372 before sending itto another summation block 376 via signal 370. Gain element 372determines the estimated mass flowrate of the water. The {dot over({circumflex over (m)}_(D) is also sent to summation block 376 viasignal 374 where it may be compared to the estimated mass flowrate ofthe water to determine the estimated mass flowrate of the cement. Thisestimated mass flowrate of the cement may be sent via signal 360 to gainelement 378 where it is multiplied by 1/(the estimated density ofcement) to determine ({dot over ({circumflex over (V)}_(D))_(c). Both({dot over ({circumflex over (V)}_(D))_(w) and ({dot over ({circumflexover (V)}_(D))_(c) may be fed to a summation block 384 via respectivesignals 380 and 382 where they may be subtracted from {dot over({circumflex over (V)}_(D), which is sent to element 384 via signal 364,to determine ({dot over ({circumflex over (V)}_(D))_(a). The disturbanceflowrates ({dot over ({circumflex over (V)}_(D))_(w), ({dot over({circumflex over (V)}_(D))_(c), and ({dot over ({circumflex over(V)}_(D))_(a) for each component may then be sent to controllers viarespective signals 358, 360, and 362 to implement respective controlschemes 352, 354, and 356.

Using the foregoing implementation, the components may be separated andthe densities of the water and cement mixture excluding entrained airfor the first mixing vessel and the second mixing vessel may becalculated from estimated parameters within the VRO in accordance withthe following equations:

$\begin{matrix}{{\hat{\rho}}_{12} = \left( \frac{{{\hat{\rho}}_{w}\left( {\hat{V}}_{1} \right)}_{w} + {{\hat{\rho}}_{c}\left( {\hat{V}}_{1} \right)}_{c}}{\left( {\hat{V}}_{1} \right)_{w} + \left( {\hat{V}}_{1} \right)_{c}} \right)} & (28) \\{{\hat{\rho}}_{s} = \left( \frac{{{\hat{\rho}}_{w}\left( {\hat{V}}_{2} \right)}_{w} + {{\hat{\rho}}_{c}\left( {\hat{V}}_{2} \right)}_{c}}{\left( {\hat{V}}_{2} \right)_{w} + \left( {\hat{V}}_{2} \right)_{c}} \right)} & (29)\end{matrix}$

FIG. 8 illustrates another embodiment of the primary components ofVolumetric Ratio Observer 386 for modeling a system in which water,cement, and air are mixed in a two-vessel mixing apparatus. TheVolumetric Ratio Observer 386 includes control schemes 388, 390, and 392for the water, the cement, and the air, respectively. Those controlschemes are very similar to the control scheme shown in FIG. 3B exceptthat the {dot over ({circumflex over (V)}₁₂ gain element may be replacedby a {dot over (V)}₁₂* gain element. Again, with the commanded inputwater flowrate {dot over (V)}_(w)* and the measured input water flowrate{dot over (V)}_(w) being known, the disturbance in water flowrate may becalculated directly. That is, the {dot over (V)}_(w) and the {dot over(V)}_(w)* may be fed via respective signals 400 and 402 to a summationblock 404 for comparing the two and thus determining the estimatedvolumetric disturbance flowrate of the water ({dot over ({circumflexover (V)}_(D))_(w).

In this embodiment, disturbances due to cement delivery and due toentrained air are provided from internal PI feedback loops on the slurrydensity in the first mixing vessel and the fluid height in the secondmixing vessel as shown. The mass disturbance flowrate {dot over({circumflex over (m)}_(D) may be calculated through a PI controllerthat compares the measured slurry density in the first mixing vessel tothe estimated density calculated from the combined water, cement, andair mixture in the first mixing vessel. More specifically, thevolumetric ratio of each component to the total materials in the firstmixing vessel may be calculated by the PI controller of each controlscheme. Those volumetric ratios may then be sent via respective signals410, 412, and 414 to respective gain elements 416, 418, and 420 formultiplying the volumetric ratios by the estimated densities of air{circumflex over (ρ)}_(a), of cement {circumflex over (ρ)}_(c), and ofwater {circumflex over (ρ)}_(w), respectively to determine the estimatedfraction of the total density in the first mixing vessel for eachcomponent. Those estimated fractions may then be summed at summationblock 422 to determine the estimated total density of the slurry{circumflex over (ρ)}₁₂ in the first mixing vessel. The measured slurrydensity {circumflex over (ρ)}₁₂ and the estimated slurry density{circumflex over (ρ)}₁₂ may be sent to a summation block 428 forcalculating the difference between the two and then to a PI controller430 for determining {dot over ({circumflex over (m)}_(D).

The ({dot over ({circumflex over (V)}_(D))_(w) computed by summationblock 404 may be multiplied by the estimated density of water by passingit to a gain element 408 for determining the estimated input massflowrate of the water before sending it to another summation block 432via signal 406 where it is subtracted from the {dot over ({circumflexover (m)}_(D). The output of summation block 432 thus may be theestimated mass flowrate of the cement. The estimated mass flowrate ofthe cement may be passed through gain element 434 where it may bemultiplied by 1/(the estimated density of cement) to determine ({dotover ({circumflex over (V)}_(D))_(c).

The total volumetric disturbance flowrate {dot over ({circumflex over(V)}_(D) may be calculated through a PI controller that compares themeasured fluid height h₂ to the estimated height ĥ₂ in the second mixingvessel calculated from the combined water, cement, and air volumes inthe second mixing vessel, assuming that its cross-sectional area isknown. More specifically, ĥ₂ may be calculated by sending the volumes ofwater, cement, and air in the second mixing vessel, as determined viacontrol schemes 388, 390, and 392, to a summation block 442 via signals436, 438, and 440, respectively. At summation block 442, those volumesmay be summed together to determine the total volume of fluid in thesecond mixing vessel. The total volume may then be sent to a gainelement 444 for multiplying it by 1/(the estimated cross-sectional areaof the second mixing vessel) to determine ĥ₂ before being sent tosummation block 450. The summation block 450 may determine thedifference between h₂ and ĥ₂, and that difference may be sent to a PIcontroller 452 via signal 451. The outputs of the integral portion andthe proportional portion of PI controller 452 may then be summed atsummation block 454 to determine the {dot over ({circumflex over(V)}_(D). Then the {dot over ({circumflex over (V)}_(D) may be sent toanother summation block 458 via signal 456. Both ({dot over ({circumflexover (V)}_(D))_(w) and ({dot over ({circumflex over (V)}_(D))_(c) may befed to a summation block 458 via respective signals 460 and 462 wherethey may be subtracted from {dot over ({circumflex over (V)}_(D) todetermine the volumetric disturbance flowrate in the air ({dot over({circumflex over (V)}_(D))_(a). The disturbance flowrates ({dot over({circumflex over (V)}_(D))_(w), ({dot over ({circumflex over(V)}_(D))_(c), and ({dot over ({circumflex over (V)}_(D))_(a) for eachcomponent may then be sent to controllers via respective signals 394,396, and 398 to implement respective control schemes 388, 390, and 392.Additionally, Equations 28 and 29 may be implemented to estimate themixture densities in the first and second mixing vessels due to waterand cement but excluding entrained air.

As shown in FIG. 9, a process for mixing multiple components in a mixingapparatus comprising a single vessel or tank may also be controlledusing a volumetric ratio mixing control scheme. In one embodiment, thecomponents being combined in the mixing apparatus may be cement andwater. However, it is understood that other materials may also becombined in the single vessel. FIG. 9 depicts a control system 500 thatincludes a Flow Regulator 502, a Height Observers 506, and a VolumetricRatio Observer 530. The Flow Regulator 502 includes a Flow Modulator 32,shown in detail in FIG. 2, a State Feedback Controller 510, and a modelof a physical system 508 similar to the physical system 34 shown in FIG.2. The physical system 508 is different from physical system 34 of FIG.2 in that it only models a single mixing vessel with the height anddensity of the mixture in the single mixing vessel given as outputs.That is, the volumetric rate of change in the mixing vessel of physicalsystem 508 is converted to the rate of change of height in the mixingvessel, which when integrated results in the height h of the slurry inthe mixing vessel. Further, the mass rate of change in the mixing vesselof physical system 508 is converted to the rate of change of the densityin the mixing vessel, which when integrated results in the density ρ ofthe slurry in the mixing vessel.

The measured height h of the slurry in the mixing vessel as given by themodel of physical system 508 may be sent to Height Observer 506, whichcontains the same components as Height Observer 132 in FIG. 6. TheHeight Observer 506 may estimate the height ĥ of the fluid in the mixingvessel and feed that to Flow Regulator 502. The measured height h mayalso be fed to Volumetric Ratio Observer 530, which is similar to theVolumetric Ratio Observer 145 shown in FIG. 6 except that it onlycontains one feedback loop for estimating the volumetric flowrate ({dotover ({circumflex over (V)}_(s))_(w) of the water exiting the mixingvessel and the ratio of water to total materials {circumflex over(R)}_(w) in the mixing vessel and one feedback loop for estimating thevolumetric flowrate ({dot over ({circumflex over (V)}_(s))_(c). TheVolumetric Ratio Observer 530 may estimate the total volumetricdisturbance flowrate {dot over ({circumflex over (V)}_(D) in the samemanner as does Volumetric Ratio Observer 145.

Turning to Flow Regulator 502, its upper portion includes a summationblock 514 to which ĥ may be sent via signal 510 and a commanded heighth* may be sent via signal 512. The summation block 514 may subtract ĥfrom h*. The output of summation block 514 may then be sent to aproportional gain element 518 via signal 516 where it may be multipliedby a constant K_(V) before being sent to another summation block 524. Acommanded volumetric flowrate {dot over (V)}_(s)* of the slurry exitingthe mixing vessel and {dot over ({circumflex over (V)}_(D) as determinedby Volumetric Ratio Observer 530 may be also be fed to summation block524 via signals 520 and 522, respectively. The summation block 514 maysubtract {dot over ({circumflex over (V)}_(D) from the sum of the outputof gain element 518 and {dot over (V)}_(s)* to determine the totalcommanded input flowrate {dot over (V)}_(in)* to the mixing vessel,which may be fed to Flow Modulator 32 via signal 526.

The lower portion of Flow Regulator 502 may include a summation block538 to which a desired water ratio R_(w)* and the estimated water ratio({circumflex over (R)}₁₂)_(w) in the first mixing vessel may be fed viasignals 538 and 532, respectively. The summation block 538 subtracts({circumflex over (R)}₁₂)_(w) from R_(w)*, and its output may then befed via signal 540 to a proportional gain element 542 for multiplyingthe output by K_(m) before being sent to a summation block 544. Theestimated output flowrate of the water ({dot over ({circumflex over(V)}_(s))_(w) from the mixing vessel also may be fed back to the FlowRegulator for decoupling purposes. That is, the ({dot over ({circumflexover (V)}_(s))_(w) may be fed via signal 534 to summation block 544where the commanded input flowrate of the water {dot over (V)}_(w)* maybe computed. The {dot over (V)}_(w)* may be fed to Flow Modulator 32 viasignal 546.

In the various embodiments shown in FIGS. 2-9, the control schemes maybe implemented by hardware or by software via a computerized system. Aperson of ordinary skill in the art would know how to create and usesuch hardware or software to implement the control schemes.

EXAMPLES

The invention having been generally described, the following examplesare given as particular embodiments of the invention and to demonstratethe practice and advantages thereof. It is understood that the examplesare given by way of illustration and are not intended to limit thespecification or the claims to follow in any manner.

The mixing apparatus shown in FIG. 1 was assembled and operated usingthe embodiment of the control scheme shown in FIG. 6. Various parametersof the mixing process were determined and plotted as a function of timein FIG. 10. More specifically, line 550, labeled as the slurryrecirculation density, represents the change in the measured slurrydensity in the first vessel. Line 552, labeled as the Ve_ densityrepresents the change in the density as given by the volumetric ratioobserver with active disturbance decoupling. Line 554, labeled as thetub level, represents the change in the height of the slurry in thesecond vessel. Line 556, labeled as the cement valve position,represents the change in the position of the valve for controlling theflowrate of the cement into the mixing apparatus. Line 558, labeled ash2_hat, represents the change in the estimated height of the slurry inthe second vessel as determined by the height observer, which filtersthe height sensor without zero lag. Line 560, labeled as the water valveposition, represents the change in the position of the valve forcontrolling the flowrate of the cement into the mixing apparatus.

The results shown in FIG. 10 illustrate that the system is capable ofcontrolling the relative volumes of cement and water in the mixing tub.Having line 550 track line 552 indicates that the system is producingthe desired density and therefore the desired relative volumes. Also,the tub level is maintained near a desired amount, showing that theflowrate is maintained near its desired amount. It should be noted thatat time 14 hr.: 17 min. the cement delivery system runs low and a newsupply is initiated. This is a common occurrence and is not a problemwith the control system.

FIG. 11 shows yet another embodiment, with a different implementation ofthe disclosed volumetric control ideas. Note the following two aspectsof this embodiment:

-   -   1) Variable height control: The height setpoint is changed        depending on the height observer error, or cement rate error.        This is done to reduce effects of water/cement ratio problems if        we have flow inconsistencies in the cement supply system. This        normally occurs when we switch between cement supply bins or        pods.    -   2) Ideal ratio control: Instead of a ratio observer outlined in        the previous embodiments this system uses the idea case by only        inputting the output flow rate and assuming all other values.

According to various embodiments, methods of determining an estimatedvolumetric ratio of a material to total materials in a mixing vesselcomprise: summing a commanded input flowrate of the material and avolumetric disturbance flowrate of the material being fed to the mixingvessel; estimating the output flowrate of the material exiting themixing vessel; negatively feeding back the estimated output flowrate ofthe material to obtain an estimated volumetric rate of change of thematerial in the mixing vessel; and integrating the estimated volumetricrate of change of the material to compute the estimated volumetric ratioof the material to the total materials in the mixing vessel.

In more embodiments, methods of determining an estimated volumetricratio of a material to total materials in a second mixing vessel that ispartially separated from a first mixing vessel comprise: summing acommanded input flowrate of the material and a volumetric disturbanceflowrate of the material being fed to the first mixing vessel;estimating an output flowrate of the material exiting the first mixingvessel; negatively feeding back the estimated output flowrate of thematerial to obtain an estimated volumetric rate of change of thematerial in the first mixing vessel; integrating the estimatedvolumetric rate of change of the material in the first mixing vessel todynamically recompute the estimated output flowrate of the materialexiting the first mixing vessel; estimating an output flowrate of thematerial exiting the second mixing vessel; negatively feeding back theestimated output flowrate of the material exiting the second mixingvessel and summing it with the estimated output flowrate of the materialexiting the first mixing vessel, thereby obtaining an estimation of avolumetric rate of change of the material in the second mixing vessel;and integrating the estimated volumetric rate of change of the materialin the second mixing vessel to compute the estimated volumetric ratio ofthe material to the total materials in the second mixing vessel.

In additional embodiments, methods of determining an estimatedvolumetric ratio of a second material to total materials in a firstmixing vessel that is partially separated from a second mixing vesselcomprise: measuring a height of the total materials in the second mixingvessel; comparing the height of the total materials in the second mixingvessel to a summation of an estimated height of a first material in thesecond mixing vessel and an estimated height of the second material inthe second mixing vessel to obtain an estimation of a height error forthe second mixing vessel; feeding the estimation of the height error toa controller to compute an estimated total volumetric disturbanceflowrate; computing a summation of (a) a commanded input flowrate of thesecond material to the first mixing vessel, (b) the estimated totalvolumetric disturbance flowrate, and (c) a negative value of anestimated output flowrate of the second material from the first mixingvessel, thereby obtaining an estimated volumetric rate of change of thesecond material in the first mixing vessel; and integrating theestimated volumetric rate of change of the second material to obtain theestimated volumetric ratio of the second material to total materials inthe first mixing vessel.

According to other embodiments, systems for determining an estimatedvolumetric ratio of a material to total materials in a mixing vesselcomprise: a summation block for determining an estimated volumetric rateof change of the material in the mixing vessel; an integration elementfor determining an estimated volume of the material in the mixing vesselbased on the estimated volumetric rate of change of the material in themixing vessel; a first gain element for converting the estimated volumeof the material in the mixing vessel to the estimated volumetric ratioof the material to the total materials; and a second gain element forconverting the estimated volumetric ratio of the material to the totalmaterials to the output flowrate of the material from the mixing vessel.

In more embodiments, systems for determining an estimated volumetricratio of a material to total materials in a second mixing vessel that ispartially separated from a first mixing vessel comprise: a firstsummation block for determining an estimated volumetric rate of changeof the material in the first mixing vessel; a first integration elementfor integrating the estimated volumetric rate of change of the materialin the first mixing vessel to determine an estimated volume of thematerial in the first mixing vessel; a first gain element for convertingthe estimated volume of the material in the first mixing vessel to theestimated volumetric ratio of the material to the total materials in thefirst mixing vessel; a second gain element for converting the estimatedvolumetric ratio of the material to the total materials in the firstmixing vessel to the output flowrate of the material from the firstmixing vessel; a second summation block for determining an estimatedvolumetric rate of change of the material in the second mixing vesselbased on the output flowrate of the material from the first mixingvessel; a second integration element for integrating the estimatedvolumetric rate of change of the material in the second mixing vessel todetermine the estimated volume of the material in the second mixingvessel; a third gain element for converting the estimated volume of thematerial in the second mixing vessel to the estimated volumetric ratioof the material to the total materials in the second mixing vessel; anda fourth gain element for converting the estimated volumetric ratio ofthe material to the total materials in the second mixing vessel to theoutput flowrate of the material from the second mixing vessel.

In yet more embodiments, systems for determining an estimated volumetricratio of a second material to total materials in a first mixing vesselthat is partially separated from a second mixing vessel comprise: asensor for measuring a height of the total materials in the secondmixing vessel; a first summation block for determining an estimation ofa height error for the second mixing vessel by comparing the height ofthe total materials in the second mixing vessel with a summation of anestimated height of a first material in the second mixing vessel and anestimated height of the second material in the second mixing vessel; acontroller for determining an estimated volumetric disturbance flowrateof the second material based on the height error; a second summationblock for determining an estimated volumetric rate of change of thesecond material in the first mixing vessel; an integration element forintegrating the estimated volumetric rate of change of the secondmaterial in the first mixing vessel to determine the estimated volume ofthe second material in the first mixing vessel; a first gain element forconverting the estimated volume of the second material in the firstmixing vessel to the estimated volumetric ratio of the material to thetotal materials in the first mixing vessel; and a second gain elementfor converting the estimated volumetric ratio of the material to thetotal materials in the first mixing vessel to an output flowrate of thematerial from the first mixing vessel.

According to additional embodiments, methods of controlling a volumetricratio of a material to total materials in a mixing vessel comprise:estimating the volumetric ratio of the material to the total materialsin the mixing vessel and an output flowrate of the material from themixing vessel using a volumetric ratio observer; dynamically recomputingthe commanded input flowrate of the material based on outputs of thevolumetric ratio observer using a flow regulator; and adjusting an inputvalve of the material based on the commanded input flowrate of thematerial using a flow modulator. In one embodiment, the mixing vesselcomprises a first mixing vessel partially separated from a second mixingvessel. In this case, a height observer may be used to estimate theheight of the total materials in the second mixing vessel, and thevolumetric ratio observer may be used to estimate the volumetric ratioof the material to the total materials in the first mixing vessel and anoutput flowrate of the material from the first mixing vessel.

In additional embodiments, methods of controlling a volumetric ratio ofa material to total materials in a first mixing vessel that is partiallyseparated from a second mixing vessel comprise: estimating thevolumetric ratio of the material to the total materials in the secondmixing vessel, an output flowrate of the material from the first mixingvessel, and a volumetric disturbance flowrate of the material using avolumetric ratio observer having the following inputs: a commanded inputflowrate of the material and a measured input flowrate of the material;computing a commanded output flowrate of the material from the firstmixing vessel using a state feedback controller having the followinginputs: a commanded volumetric ratio of the material to the totalmaterials in the second mixing vessel and the estimated volumetric ratioof the material to the total materials in the second mixing vessel;dynamically recomputing the commanded input flowrate of the materialusing a flow regulator having the following inputs: the estimated inputflowrate error of the material and the estimated output flowrate of thematerial from the first mixing vessel; and adjusting an input valve ofthe material based on the commanded input flowrate of the material usinga flow modulator.

In yet more embodiments, methods of controlling a volumetric ratio of amaterial to total materials in a first mixing vessel that is partiallyseparated from a second mixing vessel comprise: estimating a totalvolumetric disturbance flowrate, the volumetric ratio of the material tothe total materials in the first mixing vessel, and an output flowrateof the material from the first mixing vessel using a volumetric ratioobserver having the following inputs: a measured height of the totalmaterials in the second mixing vessel; a commanded input flowrate of thematerial; and a commanded input flowrate of a second material that isalso being fed to the first mixing vessel; dynamically recomputing thecommanded input flowrate of the material using a flow regulator havingthe following inputs: a commanded volumetric ratio of the material tothe total materials in the first mixing vessel; an estimated volumetricratio of the material to the total materials in the first mixing vessel;and the estimated output flowrate of the material from the first mixingvessel; and adjusting an input valve of the material based on thecommanded input flowrate of the material using a flow modulator.

According to additional embodiments, systems for controlling avolumetric ratio of a material to total materials in a mixing vesselcomprise: a volumetric ratio observer for estimating the volumetricratio of the material to the total materials in the mixing vessel and anoutput flowrate of the material from the mixing vessel; a flow regulatorcoupled to the volumetric ratio observer for dynamically recomputing acommanded input flowrate of the material based on outputs of thevolumetric ratio observer; and a flow modulator coupled to the flowregulator for adjusting an input valve of the material based on thecommanded input flowrate of the material. In one embodiment, the mixingvessel comprises a first mixing vessel partially separated from a secondmixing vessel. In this case, a height observer may be used to estimatethe height of the total materials in the second mixing vessel, and thevolumetric ratio observer may be capable of estimating the volumetricratio of the material to the total materials in the first mixing vesseland an output flowrate of the material from the first mixing vessel.

In more embodiments, systems for controlling a volumetric ratio of amaterial to total materials in a first mixing vessel that is partiallyseparated from a second mixing vessel comprise: a volumetric ratioobserver for estimating the volumetric ratio of the material to thetotal materials in the second mixing vessel, an output flowrate of thematerial from the first mixing vessel, and a volumetric disturbanceflowrate of the material, the volumetric ratio observer having thefollowing inputs: an estimated total volumetric disturbance flowrate anda commanded input flowrate of the material; a state feedback controllerfor computing a commanded output flowrate of the material from the firstmixing vessel, the state feedback controller having the followinginputs: a commanded volumetric ratio of the material to the totalmaterials in the second mixing vessel and the estimated volumetric ratioof the material to the total materials in the second mixing vessel; aflow regulator coupled to the state feedback controller and to thevolumetric ratio observer for dynamically recomputing the commandedinput flowrate of the material, the flow regulator having the followinginputs: the estimated volumetric disturbance flowrate of the materialand the estimated output flowrate of the material from the first mixingvessel; and a flow modulator coupled to the flow regulator for adjustingan input valve of the material based on the commanded input flowrate ofthe material.

In still more embodiments, systems for controlling a volumetric ratio ofa material to total materials in a first mixing vessel that is partiallyseparated from a second mixing vessel comprise: a volumetric ratioobserver for estimating a total volumetric disturbance flowrate, thevolumetric ratio of the material to the total materials in the firstmixing vessel, and an output flowrate of the material from the firstmixing vessel, the volumetric ratio observer having the followinginputs: a measured height of the total materials in the second mixingvessel; a commanded input flowrate of the material; and a commandedinput flowrate of a second material that is also being fed to the firstmixing vessel; a flow regulator coupled to the volumetric ratio observerfor dynamically recomputing a commanded input flowrate of the materialhaving the following inputs: a commanded volumetric ratio of thematerial to the total materials in the first mixing vessel; theestimated volumetric ratio of the material to the total materials in thefirst mixing vessel; and the estimated output flowrate of the materialfrom the first mixing vessel; and a flow modulator coupled to the flowregulator for adjusting an input valve of the material based on thecommanded input flowrate of the material.

In various embodiments, methods comprise: generating multiple estimatesof multiple respective component volumes; generating a feedbackcorrection using at least one physical measurement of a mixed product;and combining the feedback correction with at least mone of theestimates to provide a closed loop system. In more embodiments, methodsof controlling a mixing process comprise: in a first process, convertinghigh-level comanded inputs (e.g., the height of the slurry in a mixingvessel and the volumetric ratio of one material to the total materialsin a mixing vessel) into intermediate commanded targets (e.g. thedesired total flowrate from a mixing vessel and the desired volumetricratio of one material to the total materials in a mixing vessel); and inat least one additional process, converting the intermediate commandedtargets into low-level control settings (e.g., the valve positions),wherein a disturbance value is fed back into the first process todecouple nonlinearities. In further embodiments, methods of controllinga mixing process comprise: in a first process, converting high-levelcommanded inputs into intermediate commanded targets; in at least oneadditional process, converting the intermediate commanded targets intolow-level control settings; and using feedforward of a total flowrate todecouple effects of an output flow. In yet more embodiments, methods forcontrolling a mixing process which is affected by physicalnonlinearities comprise: compensating for the nonlinearities to providean equivalent virtual system having more stable eigenvalues; andcontrolling the mixing process with reference to the equivalent virtualsystem.

In various embodiments, systems comprise: multiple volumetric estimatorsfor multiple respective components; and a feedback block for combiningat least one physical measurement of a mixed product with the estimatorsto provide a closed loop system. In more embodiments, systems forconverting the intermediate commanded targets into low-level controlsettings, wherein the system is capable of feeding a disturbance valueback into the first process to decouple nonlinearities. In additionalembodiments, systems for controlling a mixing process comprise: a firstprocess for converting high-level commanded inputs into intermediatecommanded targets; and at least one additional process for convertingthe intermediate commanded targets into low-level control settings,wherein the system is capable of using feedforward of a total flowrateto decouple effects of an output flow. In yet more embodiments, systemsfor controlling a mixing process which is affected by physicalnonlinearities comprise: at least one low-level control loop forcontrolling inputs to the mixing process; a real-time simulation of anequivalent virtual system in which the physical nonlinearities of themixing process are at least partially compensated to provide for morestable eigenvalue behavior; and an additional control loop forcontrolling the equivalent virtual system, wherein the system is capableof using outputs of the additional control loop to at least partiallycontrol the low-level control loop.

According to various teachings of the present application, there isprovided: A method of controlling a mixing process, comprising: in afirst process, converting high-level commanded inputs into intermediatecommanded targets; and in at least one additional process, convertingsaid intermediate commanded targets into low-level control settings;wherein a disturbance value is fed back into said first process todecouple nonlinearities.

According to various teachings of the present application, there isprovided: A method of controlling a mixing process, comprising theactions of: in a first process, converting high-level commanded inputsinto intermediate commanded targets; in at least one additional process,converting said intermediate commanded targets into low-level controlsettings; and using feedforward of total flow rate to decouple effectsof output flow.

According to various teachings of the present application, there isprovided: A method for controlling a mixing process which is affected byphysical nonlinearities, comprising the actions of: compensating fornonlinearities, to provide an equivalent virtual system with more nearlystationary eigenvalues; and controlling the mixing process withreference to said equivalent virtual system.

Modifications and Variations

While preferred embodiments of the invention have been shown anddescribed, modifications thereof can be made by one skilled in the artwithout departing from the spirit and teachings of the invention. Theembodiments described herein are exemplary only and are not intended tobe limiting. Many variations and modifications of the inventiondisclosed herein are possible and are within the scope of the invention.

Various modifications, alternatives and implementations are suggestedabove, but many others are possible. For example, the observers are notnecessarily implemented as in any of the examples above, but can bemodified in various ways. For another example, the embodiments describedabove do not stand in isolation, but can be combined in various ways.

Accordingly, the scope of protection is not limited by the descriptionset out above but is only limited by the claims which follow, that scopeincluding all equivalents of the subject matter of the claims. Each andevery claim is incorporated into the specification as an embodiment ofthe present invention. Thus, the claims are a further description andare an addition to the preferred embodiments of the present invention.The discussion of a reference herein is not an admission that it isprior art to the present invention, especially any reference that mayhave a publication date after the priority date of this application. Thedisclosures of all patents, patent applications, and publications citedherein are hereby incorporated by reference, to the extent that theyprovide exemplary, procedural, or other details supplementary to thoseset forth herein.

1. A method of controlling a volumetric ratio of a first material tototal materials in a mixing vessel, comprising: estimating thevolumetric ratio of the first material to the total materials in themixing vessel and an output flowrate of the first material from themixing vessel using a volumetric ratio observer, which providesfiltered, zero-lag estimates of the actual volumetric ratios ofmaterials in the mixing vessel by mathematical modeling that includes amodeled volumetric flowrate disturbance component; dynamicallyrecomputing a commanded input flowrate of the first material based onoutputs of the volumetric ratio observer using a flow regulator; andadjusting an input valve of the first material based on the commandedinput flowrate of the material using a flow modulator that transformsthe commanded input flow rate and a commanded volumetric ratio of thefirst material to total materials into positions of the input valve, andso volumetrically control the input valve utilizing the estimatedvolumetric ratio.
 2. The method of claim 1, wherein the mixing vesselcomprises a first mixing vessel partially separated from a second mixingvessel.
 3. The method of claim 2, further comprising estimating a heightof the total materials in the second mixing vessel using a heightobserver.
 4. The method of claim 3, further comprising: estimating atotal volumetric disturbance flowrate using the height observer whichhas the following inputs: a measured height of the total materials inthe second mixing vessel; a commanded input flowrate of the totalmaterials; and a measured output flowrate of the total materials fromthe second mixing vessel; and estimating a volumetric disturbanceflowrate of the first material using the volumetric ratio observer,which has the following inputs: a measured input flowrate of the firstmaterial and a commanded input flowrate of the first material, whereinthe flow regulator has the following inputs: the estimated volumetricratio of the first material to the total materials in the first mixingvessel; the estimated volumetric disturbance flowrate of the firstmaterial; and the estimated output flowrate of the first material fromthe first mixing vessel.
 5. The method of claim 3, further comprisingestimating an output flowrate of the total materials from the firstmixing vessel using a weir flow observer having the following inputs:the estimated height of the total materials in the second mixing vessel;a measured height of the total materials in the second mixing vessel;and a measured output flowrate of the total materials from the secondmixing vessel.
 6. The method of claim 5, wherein the weir flow observercomprises a PI controller.
 7. The method of claim 6, wherein the weirflow observer further comprises an Integral controller coupled to the PIcontroller.
 8. The method of claim 3, further comprising computing acommanded output flowrate of the total materials from the first mixingvessel using a state feedback controller having the following inputs: acommanded height of the total materials in the second mixing vessel; theestimated height of the total materials in the second mixing vessel; anda commanded output flowrate of the total materials from the secondmixing vessel.
 9. The method of claim 8, further comprising dynamicallyrecomputing a commanded input flowrate of the total materials using asecond portion of a flow regulator having the following inputs: thecommanded output flowrate of the total materials from the first mixingvessel; an estimated output flowrate of the total materials from thefirst mixing vessel; and an estimated volumetric disturbance flowrate.10. The method of claim 9, further comprising adjusting an input valvefor a second material based on the commanded input flowrate of the totalmaterials and the commanded input flowrate of the material using theflow modulator.
 11. The method of claim 2, wherein the volumetric ratioobserver is used to estimate the volumetric ratio of the first materialto the total materials in the first mixing vessel and an output flowrateof the material from the first mixing vessel.
 12. The method of claim 2,wherein the volumetric ratio observer has a total volumetric disturbanceflowrate as another input, and wherein it is also used to estimate thevolume of the total materials in the first mixing vessel.
 13. The methodof claim 2, wherein the height observer comprises a PI controller. 14.The method of claim 13, wherein the height observer further comprises anIntegral controller coupled to the PI controller.
 15. The method ofclaim 2, wherein the volumetric ratio observer comprises first andsecond Integral controllers.
 16. The method of claim 1, wherein thetotal materials comprise water and cement.
 17. The method of claim 1,being implemented by a computerized system or by hardware.
 18. Themethod of claim 1, wherein the total materials comprise a fluid and agas-transported dry material.
 19. A method of controlling a volumetricratio of a first material to total materials in a first mixing vesselthat is partially separated from a second mixing vessel, comprising:estimating the volumetric ratio of the first material to the totalmaterials in the second mixing vessel, an output flowrate of the firstmaterial from the first mixing vessel, and a volumetric disturbanceflowrate of the first material using a volumetric ratio observer havingthe following inputs: a commanded input flowrate of the first materialand a measured input flowrate of the first material; computing acommanded output flowrate of the first material from the first mixingvessel using a state feedback controller having the following inputs: acommanded volumetric ratio of the first material to the total materialsin the second mixing vessel and the estimated volumetric ratio of thefirst material to the total materials in the second mixing vessel;dynamically recomputing the commanded input flowrate of the firstmaterial using a flow regulator having the following inputs: anestimated input flowrate error of the first material and the estimatedoutput flowrate of the first material from the first mixing vessel; andadjusting an input valve of the first material based on the commandedinput flowrate of the first material using a flow modulator thattransforms the commanded input flow rate and the commanded volumetricratio of the first material to total materials into positions of theinput valve, and so volumetrically control the input valve utilizing theestimated volumetric ratio; wherein the volumetric ratio observerprovides filtered, zero-lag estimates of the actual volumetric ratios ofmaterials in the second mixing vessel by mathematical modeling thatincludes a modeled volumetric flowrate disturbance component.
 20. Amethod of controlling a volumetric ratio of a first material to totalmaterials in a first mixing vessel that is partially separated from asecond mixing vessel, comprising: estimating a total volumetricdisturbance flowrate, the volumetric ratio of the first material to thetotal materials in the first mixing vessel, and an output flowrate ofthe first material from the first mixing vessel using a volumetric ratioobserver having the following inputs: a measured height of the totalmaterials in the second mixing vessel; a measured input flowrate of thefirst material; and a commanded input flowrate of a second material thatis also being fed to the first mixing vessel; dynamically recomputing acommanded input flowrate of the first material using a flow regulatorhaving the following inputs: a commanded volumetric ratio of the firstmaterial to the total materials in the first mixing vessel; an estimatedvolumetric ratio of the first material to the total materials in thefirst mixing vessel; and the estimated output flowrate of the firstmaterial from the first mixing vessel; and adjusting an input valve ofthe first material based on the commanded input flowrate of the firstmaterial using a flow modulator that transforms a commanded input flowrate and the commanded volumetric ratio of the first material to totalmaterials into positions of the input valve, and so volumetricallycontrol the input valve utilizing the estimated volumetric ratio;wherein the volumetric ratio observer provides filtered, zero-lagestimates of the actual volumetric ratios of materials in the firstmixing vessel by mathematical modeling that includes a modeledvolumetric flowrate disturbance component.